This analysis was prepared by Francisco Arrieta and Jonathan Edwards.

1 Setup

# options(scipen=999) #prevent scientific notation
# options(scipen=-999) #encourage scientific notation
options(scipen=0) #encourage scientific notation neutral?

# kable table layout options
# do not display NAs and only 2 digits
opts <- options(knitr.kable.NA = '') #knitr.table.format = "latex"

# define table styling options
stable <- function(data, digits = 2) {
  knitr::kable(data, digits=digits) |> 
    # kable_styling(c("striped", "condensed"))
    kable_paper(full_width = F)
}

1.1 libraries

# modelling
library(psych) #factor analysis tools (PAF PAF)
library(lavaan) #causal analysis
library(lm.beta) # add standarized regression coeffs

# stats
library(nortest) #Kolmogorov-Smirnov-Test
library(corrplot) #correlation matrix plot
library(olsrr)  #VIF and Tolerance Values
library(pastecs) # provides function stat.desc
library(REdaS) #Bartelett's Test

# plotting & formatting
library(ggplot2) #better graphs
library(patchwork) # provides wrap_plots for multiplotting 
# library(gridExtra) #provides multiplotting functionality
# library(ggpubr) #provides ggarrange for multiplotting (patchwork better though)
library(semPlot) #for visualization of path diagrams (SEM)
library(lavaanPlot) #for visualization of path diagrams (SEM)
# library(rcompanion)   #Histogram and Normal Curve
library(kableExtra) #makes nice tables

# generic
library(dplyr) #useful data manip functions like arrange, distinct, rename etc included in fpp3
library(stringr) # provides string manip functions like str_split_fixed 
library(Hmisc) #describe function that describes features of dataframes
library(data.table) # creating and manipulating datatables
library(knitr) #rmarkdown tools not sure why useful
library(parameters) #get model outputs in table form (good for making tabs)

1.2 Load data

survey <- read.csv("Case Study III_Structural Equation Modeling.csv")
labels <- read.csv("Variables and Labels_Galeries Lafayette.csv")

dim(survey)

## [1] 553  45

# head(labels)

1.3 labels

#Make labels more readable
#create copy of label column without variable code
labels["Category"] <- sub("[^-]*\\s-","",labels[["Label"]]) 
# labels["Category"] <- sub(".*\\s-","",labels[["Label"]])
# labels

#split this new column (category) into category and short label
labels[c("Category","Label_short")] <- str_split_fixed(labels[["Category"]],"\\?\\s\\s|\\s-", n=2)
# labels[20:25,c("Category","Label_short")]
labels[,c("Variable","Category","Label_short")] |>
  stable()

Variable	Category	Label_short
Im1	What do GLB represent from your point of view	Large Assortment
Im2	What do GLB represent from your point of view	Assortment Variety
Im3	What do GLB represent from your point of view	Artistic Decoration of Sales Area
Im4	What do GLB represent from your point of view	Creative Decoration of Sales Area
Im5	What do GLB represent from your point of view	Appealing Arrangement of Shop Windows
Im6	What do GLB represent from your point of view	France
Im7	What do GLB represent from your point of view	French Savoir-vivre
Im8	What do GLB represent from your point of view	Expertise in French Traditional Cuisine
Im9	What do GLB represent from your point of view	French Fashion
Im10	What do GLB represent from your point of view	Gourmet Food
Im11	What do GLB represent from your point of view	High-quality Cosmetics
Im12	What do GLB represent from your point of view	Luxury brands
Im13	What do GLB represent from your point of view	Up tp date Designer Brands
Im14	What do GLB represent from your point of view	Gourmet specialities
Im15	What do GLB represent from your point of view	Professional Selection of Brands
Im16	What do GLB represent from your point of view	Professional Appearance Towards Customers
Im17	What do GLB represent from your point of view	Are Trendy
Im18	What do GLB represent from your point of view	Are Hip
Im19	What do GLB represent from your point of view	Professional Organization
Im20	What do GLB represent from your point of view	Relaxing Shopping
Im21	What do GLB represent from your point of view	A Great Place to Stroll
Im22	What do GLB represent from your point of view	Intimate Shop Atmosphere
C_CR1	CO-CREATION	I would like to participate in an expert-workshop to improve the assortment of Galeries Lafayette Berlin.
C_CR2	CO-CREATION	I would be available to take part in another survey at Galeries Lafayette Berlin.
C_CR3	CO-CREATION	I would like to become a member of a customer group whose opinion is obtained for new products and major changes.
C_CR4	CO-CREATION	I would like to participate in planning and designing special events (e.g. fashion show, introduction of new car models) if asked.
C_REP1	REPURCHASE	I will continue to be a loyal customer of Galeries Lafayette Berlin.
C_REP2	REPURCHASE	I intend to shop at Galeries Lafayette Berlin in the future.
C_REP3	REPURCAHSE	I will surely visit Galeries Lafayette Berlin in the future.
COM_A1	AFFECTIVE COMMITMENT	How strongly are you attached to Galeries Lafayette Berlin?
COM_A2	AFFECTIVE COMMITMENT	How strongly are you emotionally connected to Galeries Lafayette Berlin?
COM_A3	AFFECTIVE COMMITMENT	As a customer I feel (close) attached to GL
COM_A4	AFFECTIVE COMMITMENT	feel a strong emotional bond toward GLB
SAT_1	SATISFACTION	I am very satisfied with Galeries Lafayette Berlin.
SAT_2	SATISFACTION	Overall, I am very satisfied with Galeries Lafayette Berlin.
SAT_3	SATISFACTION	How satisfied are you with Galeries Lafayette Berlin?
SAT_P1	SATISFACTION EMPLOYEES	The employees are capable and professional.
SAT_P2	SATISFACTION EMPLOYEES	The employees know best about their products.
SAT_P3	SATISFACTION EMPLOYEES	The employees are well-informed.
SAT_P4	SATISFACTION EMPLOYEES	The employees are always helpful.
SAT_P5	SATISFACTION EMPLOYEES	The employees are willing to respond to my questions in detail.
SAT_P6	SATISFACTION EMPLOYEES	The employees are friendly.
TRU_1	TRUST	I have the feeling that I can completely rely on GL.
TRU_2	TRUST	GLB will always be honest and trustful with me.
TRU_3	TRUST	GL will treat me always fair as a customer

1.4 Clean and handle missing data

# # omit all unanswered
# filter_all(survey, all_vars(. != 999))
# filter_all(survey, any_vars(. %in% c(999)))
# 
# filter_all(select(survey,1:22,"SAT_1"), all_vars(. != 999))
# filter_all(select(survey,1:22,"SAT_1"), any_vars(. %in% c(999)))
# 
# filter_all(data_img_EFA, all_vars(. != 999))
# filter_all(ges, any_vars(. %in% c(999)))

# delete variables unused in analysis (see case study instructions): 
survey <- survey |> select(-c("C_CR2", "SAT_P1", "SAT_P2", "SAT_P3", "SAT_P4", "SAT_P5", "SAT_P6", "TRU_1", "TRU_2", "TRU_3"))

# replace missing data (999) with NA
survey <- data.frame(sapply(survey,function(x) ifelse((x==999),NA,as.numeric(x))))

1.5 Explore Data

2 Dimensions by which Galeries Lafayette is perceived

2.1 ROUND 1: Exploratory factor analysis

2.1.1 Variable selection for EFA

# excluded image variables (in the first round of EFA we don't exclude any image variables...)
exclude=c() 

# the full survey data (includes dependent and independent variables) with excluded image variables (in this first round of EFA we don't exclude anything)
survey_excl_img <- survey |> select(-exclude)

# the data we will use for EFA (images)
data_img_EFA <- survey_excl_img[1:(22-length(exclude))]

2.1.2 handle missing data

# delete missing data (delete listwise)
data_img_EFA <- na.omit(data_img_EFA)

dim(survey)

## [1] 553  35

dim(survey_excl_img)

## [1] 553  35

dim(data_img_EFA)

## [1] 385  22

2.1.3 Check adequacy of correlation Matrix

2.1.3.1 correlation matrix

#plot correlation matrix adjusting parameters to see previously identified groupings
corr_matrix <- cor(data_img_EFA)
corrplot(as.matrix(corr_matrix), 
         method = "color", #col = c("white","white","white","white","white", "lightgrey", "darkgrey", "black"),
         order = "hclust", addrect = 10, rect.col="black", # rect.col="red",
         addCoef.col = 'black', number.cex = .5,
         tl.col ="black", 
         tl.cex = 0.80, 
         )

Variables to look out for going forward:

Images 9 and 11 are alone
Pairs of images: (17,18), cluster exclusively together, have a very high correlation and similar correlation profiles meaning we might only want to keep one of them. Similar comment to a lesser degree for (6,7) and (16,19).

2.1.3.2 Bartlett’s Test

bart_spher(data_img_EFA)

##  Bartlett's Test of Sphericity
## 
## Call: bart_spher(x = data_img_EFA)
## 
##      X2 = 6451.238
##      df = 231
## p-value < 2.22e-16

The Bartlett Test tests the hypothesis that the sample originates from a population, where all variables are uncorrelated. This would not be good for factor analysis, we want this hypothesis to be rejected meaning p-value < 5%.

In our case we see that it is indeed rejected and that the data is not uncorrelated.

2.1.3.3 KMO

KMOTEST=KMOS(data_img_EFA)
print(KMOTEST, sort=T)

## 
## Kaiser-Meyer-Olkin Statistics
## 
## Call: KMOS(x = data_img_EFA)
## 
## Measures of Sampling Adequacy (MSA):
##       Im2       Im6       Im1      Im20      Im14      Im10       Im7       Im4 
## 0.8224640 0.8224827 0.8244624 0.8266391 0.8267452 0.8285789 0.8448231 0.8542604 
##      Im18       Im3      Im17      Im13      Im12      Im22      Im16      Im11 
## 0.8550678 0.8640362 0.8644991 0.8722220 0.8789413 0.8793157 0.9092200 0.9113882 
##      Im21       Im8       Im9      Im19       Im5      Im15 
## 0.9149654 0.9300079 0.9380091 0.9400714 0.9546668 0.9647563 
## 
## KMO-Criterion: 0.8770975

The KMO of 0.8770975 is above 0.6 which indicates the data is well suited for factor anlysis.

2.1.3.4 Anti-image Correlation

MSA_list <- data.table("Item"=names(KMOTEST$MSA), "MSA"=as.numeric(KMOTEST$MSA))

# Sort table
MSA_list<- MSA_list |> 
  setorder(cols = "MSA")

# Display table
MSA_list |> 
  stable() |>
  row_spec(which(MSA_list[,2]<0.5), bold = T, color = "white", background = "#78BE20")

Item	MSA
Im2	0.82
Im6	0.82
Im1	0.82
Im20	0.83
Im14	0.83
Im10	0.83
Im7	0.84
Im4	0.85
Im18	0.86
Im3	0.86
Im17	0.86
Im13	0.87
Im12	0.88
Im22	0.88
Im16	0.91
Im11	0.91
Im21	0.91
Im8	0.93
Im9	0.94
Im19	0.94
Im5	0.95
Im15	0.96

Variables with MSA values above 0.5 are suited for factor analysis. Presence of items with low MSA’s (<0.5) could also indicate that an important topic hasn’t been well covered in the questionnaire.

All variables have MSA above 0.5

2.1.4 Select method: PAF

2.1.4.1 Extract factors

EFA_PAF0 <- psych::fa(data_img_EFA, rotate="varimax", scores=TRUE)
# note: by default number of factors = 1 if it is not specified

2.1.4.1.1 Scree plot

#display Scree-plot
plot(EFA_PAF0$e.values,xlab="Factor Number",
     ylab="Eigenvalue",
     main="Scree plot",
     cex.lab=1.2,
     cex.axis=1.2,
     cex.main=1.8,
     col = "#0099F8",
     pch = 19) 
abline(h=1, col = "#7F35B2")

2.1.4.1.2 Kaiser Criterion

EFA_PAF0_kaiser_nb <- length(which(EFA_PAF0$e.values > 1))
EFA_PAF0_kaiser_nb

## [1] 6

The Kaiser criterion suggests we should retain factors with eigenvalues bigger than 1.

There are 6 factors satisfying this condition.

2.1.4.1.3 Total Variance Explained

#calculate total variance (does not change if number of factors change)
EFA_PAF0_EigenValue <- EFA_PAF0$e.values
EFA_PAF0_Variance <- EFA_PAF0_EigenValue / ncol(data_img_EFA) * 100
EFA_PAF0_SumVariance <- cumsum(EFA_PAF0_EigenValue / ncol(data_img_EFA))
EFA_PAF0_Total_Variance_Explained <- cbind("Factor number"=
                                            seq(1, length.out=length(EFA_PAF0_EigenValue[EFA_PAF0_EigenValue>0])),
                                          EigenValue = EFA_PAF0_EigenValue[EFA_PAF0_EigenValue>0],
                                          Variance = EFA_PAF0_Variance[EFA_PAF0_EigenValue>0],
                                          Total_Variance = EFA_PAF0_SumVariance[EFA_PAF0_EigenValue>0])
#display table
EFA_PAF0_Total_Variance_Explained |> 
  stable()

Factor number	EigenValue	Variance	Total_Variance
1	8.98	40.81	0.41
2	2.47	11.21	0.52
3	1.56	7.10	0.59
4	1.46	6.62	0.66
5	1.25	5.67	0.71
6	1.15	5.22	0.77
7	0.81	3.68	0.80
8	0.71	3.23	0.84
9	0.57	2.58	0.86
10	0.46	2.08	0.88
11	0.36	1.64	0.90
12	0.33	1.51	0.91
13	0.29	1.34	0.93
14	0.28	1.29	0.94
15	0.25	1.13	0.95
16	0.23	1.04	0.96
17	0.20	0.92	0.97
18	0.19	0.85	0.98
19	0.16	0.72	0.99
20	0.12	0.53	0.99
21	0.10	0.46	1.00
22	0.08	0.37	1.00

With 6 factors we would explain 76.6310791% of total variance.

With 7 factors we would explain 80.3133487% of total variance.

# test eigenvalue calculation
factorloadings = EFA_PAF0$loadings[,1] # loadings 1st factor (default is nfactors = 1)
Eigenvalue = sum(factorloadings^2)
Eigenvalue

## [1] 8.377985

2.1.4.2 Determine number of factors to retain

# select nb of factors to test
nf = c(5,6,7,8)

2.1.4.3 PAF orthogonal Varimax with n factors

# perform multiple PAFs one for each factor number in selection
EFA_PAFn = list()

i=1
for (n in nf) {
  # EFA_PAFn[[i]] <- n
  EFA_PAFn[[i]] <- psych::fa(data_img_EFA, rotate="varimax", scores=TRUE, nfactors = n)
  i=i+1
}
names(EFA_PAFn) <- nf

2.1.4.3.1 Communalities

#communalities for all selected number of factors

for (i in 1:length(nf)) {

  cat("###### Number of factors =", nf[[i]], "{.unnumbered}" ,"\n")
  
    EFA_PAFn_communalities <- data.table("Item"=names(EFA_PAFn[[i]]$communality), 
                             "Communality"=as.numeric(EFA_PAFn[[i]]$communality))

    # Sort table
    EFA_PAFn_communalities <- EFA_PAFn_communalities |>
      setorder(cols = "Communality")
    
    # Display table
    kbl <- EFA_PAFn_communalities |> 
              stable() |>
              row_spec(which(EFA_PAFn_communalities[,1]<.3), bold = T, color = "white", background = "#78BE20")
    
    print(kbl)
    cat("\n\n")

    # test communality calculation
    variableloading = EFA_PAFn[[i]]$loadings["Im9",] # loadings 1st variable
    communality = sum(variableloading^2)
    print(paste0("Communality for Im9 =", communality))
    cat("\n")
    
}

Number of factors = 5

Item	Communality
Im9	0.41
Im11	0.41
Im18	0.43
Im16	0.46
Im6	0.50
Im19	0.53
Im17	0.54
Im5	0.55
Im15	0.63
Im21	0.65
Im14	0.66
Im10	0.66
Im7	0.69
Im20	0.69
Im12	0.71
Im13	0.72
Im2	0.76
Im8	0.76
Im22	0.81
Im1	0.82
Im3	0.86
Im4	0.92

[1] “Communality for Im9 =0.405600881872799”

Number of factors = 6

Item	Communality
Im11	0.45
Im9	0.46
Im16	0.47
Im19	0.52
Im5	0.55
Im18	0.57
Im15	0.63
Im21	0.65
Im17	0.70
Im13	0.70
Im6	0.71
Im12	0.73
Im8	0.74
Im14	0.76
Im2	0.76
Im10	0.78
Im7	0.78
Im20	0.79
Im22	0.79
Im1	0.84
Im3	0.85
Im4	0.92

[1] “Communality for Im9 =0.463399199002637”

Number of factors = 7

Item	Communality
Im11	0.44
Im9	0.46
Im16	0.47
Im19	0.53
Im5	0.54
Im15	0.63
Im21	0.65
Im13	0.70
Im18	0.71
Im8	0.72
Im6	0.76
Im2	0.78
Im22	0.79
Im20	0.79
Im14	0.81
Im12	0.83
Im7	0.85
Im1	0.86
Im3	0.86
Im10	0.89
Im17	0.95
Im4	0.97

[1] “Communality for Im9 =0.455673655610471”

Number of factors = 8

Item	Communality
Im11	0.45
Im9	0.46
Im5	0.58
Im19	0.62
Im15	0.65
Im21	0.65
Im13	0.70
Im8	0.72
Im18	0.74
Im6	0.76
Im22	0.78
Im16	0.80
Im2	0.81
Im20	0.81
Im12	0.84
Im7	0.85
Im14	0.85
Im3	0.86
Im10	0.90
Im17	0.93
Im1	0.94
Im4	0.97

[1] “Communality for Im9 =0.455554069181416”

Typically we should think about excluding variables with communalities below 0.3.

Based on the above, no variable should be excluded.

2.1.4.3.2 Factor loadings

# loadings for all selected number of factors

for (i in 1:length(nf)) {
  
cat("###### Number of factors =", nf[[i]], "{.unnumbered}" ,"\n")
  
      # print(EFA_PAFn[[i]]$loadings, cutoff=0.3)
      # print(print_html(model_parameters(EFA_PAFn[[i]], loadings=T, threshold = 0.3, summary=T)))
     kbl <- model_parameters(EFA_PAFn[[i]], loadings=T, threshold = 0.3, summary=T) |>
        stable()
     print(kbl)
      
cat("\n\n")
}

Number of factors = 5

Variable	MR2	MR5	MR4	MR1	MR3	Complexity	Uniqueness
Im1		0.85				1.31	0.18
Im2		0.83				1.23	0.24
Im3				0.83		1.55	0.14
Im4				0.87		1.46	0.08
Im5				0.64		1.78	0.45
Im6	0.67					1.22	0.50
Im7	0.79					1.20	0.31
Im8	0.84					1.16	0.24
Im9	0.43		0.39			2.76	0.59
Im10	0.75					1.37	0.34
Im11			0.57			1.56	0.59
Im12			0.79			1.27	0.29
Im13			0.77			1.43	0.28
Im14	0.75					1.37	0.34
Im15		0.60	0.33			2.66	0.37
Im16		0.48		0.37		2.77	0.54
Im17		0.38	0.48			3.44	0.46
Im18		0.31	0.43			3.42	0.57
Im19		0.47		0.40		3.37	0.47
Im20					0.78	1.27	0.31
Im21					0.74	1.41	0.35
Im22					0.81	1.51	0.19

Number of factors = 6

Variable	MR2	MR5	MR1	MR4	MR3	MR6	Complexity	Uniqueness
Im1		0.86					1.30	0.16
Im2		0.83					1.24	0.24
Im3			0.83				1.51	0.15
Im4			0.88				1.42	0.08
Im5			0.64				1.74	0.45
Im6	0.61					0.56	2.12	0.29
Im7	0.72					0.48	1.88	0.22
Im8	0.81						1.25	0.26
Im9	0.35			0.32		0.43	3.51	0.54
Im10	0.80						1.42	0.22
Im11				0.59			1.62	0.55
Im12				0.79			1.34	0.27
Im13				0.73			1.66	0.30
Im14	0.80						1.42	0.24
Im15		0.60					2.76	0.37
Im16		0.48	0.37				2.78	0.53
Im17		0.35	0.31	0.39		0.54	3.66	0.30
Im18				0.35		0.50	3.48	0.43
Im19		0.46	0.40				3.45	0.48
Im20					0.84		1.22	0.21
Im21					0.73		1.43	0.35
Im22					0.79		1.60	0.21

Number of factors = 7

Variable	MR5	MR1	MR3	MR2	MR4	MR7	MR6	Complexity	Uniqueness
Im1	0.86							1.33	0.14
Im2	0.83							1.27	0.22
Im3		0.83						1.56	0.14
Im4		0.90						1.40	0.03
Im5		0.63						1.85	0.46
Im6						0.83		1.25	0.24
Im7				0.32		0.84		1.44	0.15
Im8				0.63		0.51		2.31	0.28
Im9					0.33	0.45		3.45	0.54
Im10				0.87				1.35	0.11
Im11					0.58			1.72	0.56
Im12					0.85			1.30	0.17
Im13					0.72			1.81	0.30
Im14				0.81				1.50	0.19
Im15	0.59							2.97	0.37
Im16	0.46	0.34						3.44	0.53
Im17							0.84	1.76	0.05
Im18							0.72	1.85	0.29
Im19	0.43	0.37						4.25	0.47
Im20			0.85					1.21	0.21
Im21			0.73					1.44	0.35
Im22			0.78					1.62	0.21

Number of factors = 8

Variable	MR1	MR3	MR4	MR7	MR2	MR5	MR6	MR8	Complexity	Uniqueness
Im1						0.88			1.45	0.06
Im2						0.82			1.45	0.19
Im3	0.81								1.66	0.14
Im4	0.89								1.47	0.03
Im5	0.65								1.84	0.42
Im6				0.83					1.23	0.24
Im7				0.84	0.30				1.40	0.15
Im8				0.54	0.59				2.56	0.28
Im9			0.33	0.46					3.34	0.54
Im10					0.87				1.41	0.10
Im11			0.58						1.72	0.55
Im12			0.86						1.28	0.16
Im13			0.72						1.78	0.30
Im14					0.83				1.49	0.15
Im15						0.47		0.39	4.81	0.35
Im16								0.77	1.78	0.20
Im17							0.82		1.82	0.07
Im18							0.74		1.76	0.26
Im19	0.30							0.54	3.68	0.38
Im20		0.86							1.20	0.19
Im21		0.73							1.44	0.35
Im22		0.78							1.63	0.22

Factor loadings:

Number of items per factor >=3
- this condition is respected in all cases except when we have 8 factors. We eliminate the 8 factor solution
0.40–0.30–0.20 rule: satisfactory variables (a) load onto their primary factor above 0.40, (b) load onto alter-native factors below 0.30, and (c) demonstrate a difference of 0.20 between their primary and alternative factor loadings.
- 5 factor solution:
  - this condition is not respected for many variables. We eliminate the 5 factor solution
- 6 factor solution:
  - this condition is not respected for: Im6, Im7, Im9, (Im11), (Im15), Im16, Im17, Im18, Im19 where Im17 and Im18 are particularly spread out
- 7 factor solution:
  - this condition is not respected for: Im7, Im8, Im9, Im15, Im16, Im19 where Im16 and Im19 are particularly spread out

Based on the above we will prefer the 7 factor solution but we will no doubt have to exclude some variables.

Looking at the correlation matrix, we saw that variables Im16 and Im19 were highly correlated, we probably only need to exclude one of the two, Im19 has the lower communality of the two so we might consider eliminating that one.

Similarly Im17 and Im18 are highly correlated we might want to eliminate Im18 which has the lowest communality of the two, but they have adequately high loadings in the 7 factor solution so not a priority.

We might also exclude Im9 and Im15 as their communality is on the lower end and their loadings are spread out and quite weak. Also Im9 is problematic in both the 6 and 7 factor solution

Thurstone simple structure criteria:

Each row (variable) of the factor pattern matrix should have at least one zero
Each column (factor) should have at least r zero elements, and the zeros for one factor should be unique from the zeros for the other factors
For every pair of columns (factors), there should be at least r variables with a zero coefficient in one column and a non-zero coefficient in the other
When r > 3 every pair of columns (factors), should contain a large proportion of variables with zeros in both columns
For every pair of columns (factors), there should be only a small proportion of variables with non-zeros in both columns

2.1.4.4 PAF oblique Promax with n factors

# perform multiple PAFs one for each factor number in selection
EFA_PAFn_obl = list()

i=1
for (n in nf) {
  # EFA_PAFn_obl[[i]] <- n
  EFA_PAFn_obl[[i]] <- psych::fa(data_img_EFA, rotate="promax", scores=TRUE, nfactors = n)
  i=i+1
}
names(EFA_PAFn_obl) <- nf

length(EFA_PAFn_obl)

## [1] 4

2.1.4.4.1 Communalities

#communalities for all selected number of factors

for (i in 1:length(nf)) {

  cat("###### Number of factors =", nf[[i]], "{.unnumbered}" ,"\n")
  
    EFA_PAFn_obl_communalities <- data.table("Item"=names(EFA_PAFn_obl[[i]]$communality), 
                             "Communality"=as.numeric(EFA_PAFn_obl[[i]]$communality))

    # Sort table
    EFA_PAFn_obl_communalities <- EFA_PAFn_obl_communalities |>
      setorder(cols = "Communality")
    
    # Display table  
    kbl <- EFA_PAFn_obl_communalities |> 
              stable() |> 
              row_spec(which(EFA_PAFn_obl_communalities[,1]<.3), bold = T, color = "white", background = "#78BE20")
    
    print(kbl)
    cat("\n\n")

    # test communality calculation
    variableloading = EFA_PAFn_obl[[i]]$loadings["Im9",] # loadings 1st variable
    communality = sum(variableloading^2)
    print(paste0("Communality for Im9 =", communality))
    cat("\n")
    
}

Number of factors = 5

Item	Communality
Im9	0.41
Im11	0.41
Im18	0.43
Im16	0.46
Im6	0.50
Im19	0.53
Im17	0.54
Im5	0.55
Im15	0.63
Im21	0.65
Im14	0.66
Im10	0.66
Im7	0.69
Im20	0.69
Im12	0.71
Im13	0.72
Im2	0.76
Im8	0.76
Im22	0.81
Im1	0.82
Im3	0.86
Im4	0.92

[1] “Communality for Im9 =0.272947652560888”

Number of factors = 6

Item	Communality
Im11	0.45
Im9	0.46
Im16	0.47
Im19	0.52
Im5	0.55
Im18	0.57
Im15	0.63
Im21	0.65
Im17	0.70
Im13	0.70
Im6	0.71
Im12	0.73
Im8	0.74
Im14	0.76
Im2	0.76
Im10	0.78
Im7	0.78
Im20	0.79
Im22	0.79
Im1	0.84
Im3	0.85
Im4	0.92

[1] “Communality for Im9 =0.339338697735652”

Number of factors = 7

Item	Communality
Im11	0.44
Im9	0.46
Im16	0.47
Im19	0.53
Im5	0.54
Im15	0.63
Im21	0.65
Im13	0.70
Im18	0.71
Im8	0.72
Im6	0.76
Im2	0.78
Im22	0.79
Im20	0.79
Im14	0.81
Im12	0.83
Im7	0.85
Im1	0.86
Im3	0.86
Im10	0.89
Im17	0.95
Im4	0.97

[1] “Communality for Im9 =0.279736181915467”

Number of factors = 8

Item	Communality
Im11	0.45
Im9	0.46
Im5	0.58
Im19	0.62
Im15	0.65
Im21	0.65
Im13	0.70
Im8	0.72
Im18	0.74
Im6	0.76
Im22	0.78
Im16	0.80
Im2	0.81
Im20	0.81
Im12	0.84
Im7	0.85
Im14	0.85
Im3	0.86
Im10	0.90
Im17	0.93
Im1	0.94
Im4	0.97

[1] “Communality for Im9 =0.302814913694533”

2.1.4.4.2 Factor loadings

# loadings for all selected number of factors

for (i in 1:length(nf)) {
  
cat("###### Number of factors =", nf[[i]], "{.unnumbered}" ,"\n")
  
      # print(EFA_PAFn_obl[[i]]$loadings, cutoff=0.3)
      # print(print_html(model_parameters(EFA_PAFn_obl[[i]], loadings=T, threshold = 0.3, summary=T)))
     kbl <- model_parameters(EFA_PAFn_obl[[i]], loadings=T, threshold = 0.3, summary=T) |>
        stable()
     print(kbl)
      
cat("\n\n")
}

Number of factors = 5

Variable	MR2	MR5	MR1	MR4	MR3	Complexity	Uniqueness
Im1		1.07				1.06	0.18
Im2		1.07				1.07	0.24
Im3			1.00			1.03	0.14
Im4			1.07			1.03	0.08
Im5			0.75			1.03	0.45
Im6	0.73					1.11	0.50
Im7	0.87					1.14	0.31
Im8	0.91					1.01	0.24
Im9	0.36			0.37		2.10	0.59
Im10	0.77					1.17	0.34
Im11				0.69		1.08	0.59
Im12				1.00		1.05	0.29
Im13				0.94		1.03	0.28
Im14	0.77					1.12	0.34
Im15		0.62				1.14	0.37
Im16		0.47				1.79	0.54
Im17				0.42		2.05	0.46
Im18				0.39		1.93	0.57
Im19		0.41				2.02	0.47
Im20					0.86	1.04	0.31
Im21					0.79	1.09	0.35
Im22					0.85	1.02	0.19

Number of factors = 6

Variable	MR2	MR5	MR1	MR4	MR3	MR6	Complexity	Uniqueness
Im1		1.05					1.06	0.16
Im2		1.03					1.07	0.24
Im3			0.99				1.03	0.15
Im4			1.06				1.05	0.08
Im5			0.74				1.03	0.45
Im6	0.52					0.68	2.22	0.29
Im7	0.65					0.56	2.24	0.22
Im8	0.80						1.05	0.26
Im9						0.48	1.95	0.54
Im10	0.81						1.23	0.22
Im11				0.67			1.15	0.55
Im12				0.91			1.03	0.27
Im13				0.79			1.09	0.30
Im14	0.80						1.18	0.24
Im15		0.60					1.18	0.37
Im16		0.46					1.81	0.53
Im17						0.57	1.97	0.30
Im18						0.54	1.91	0.43
Im19		0.39					2.15	0.48
Im20					0.92		1.07	0.21
Im21					0.76		1.07	0.35
Im22					0.80		1.04	0.21

Number of factors = 7

Variable	MR5	MR1	MR2	MR3	MR4	MR7	MR6	Complexity	Uniqueness
Im1	1.08							1.06	0.14
Im2	1.05							1.06	0.22
Im3		1.00						1.02	0.14
Im4		1.13						1.04	0.03
Im5		0.72						1.02	0.46
Im6						0.92		1.06	0.24
Im7						0.89		1.06	0.15
Im8			0.62			0.38		1.74	0.28
Im9						0.42		2.10	0.54
Im10			1.04					1.03	0.11
Im11					0.65			1.14	0.56
Im12					1.01			1.04	0.17
Im13					0.78			1.08	0.30
Im14			0.94					1.01	0.19
Im15	0.60							1.17	0.37
Im16	0.40							2.69	0.53
Im17							1.09	1.02	0.05
Im18							0.92	1.02	0.29
Im19	0.33							3.23	0.47
Im20				0.94				1.05	0.21
Im21				0.78				1.06	0.35
Im22				0.81				1.05	0.21

Number of factors = 8

Variable	MR1	MR3	MR7	MR2	MR4	MR5	MR6	MR8	Complexity	Uniqueness
Im1						1.04			1.01	0.06
Im2						0.95			1.02	0.19
Im3	0.90								1.02	0.14
Im4	1.03								1.03	0.03
Im5	0.72								1.11	0.42
Im6			0.98						1.06	0.24
Im7			0.95						1.05	0.15
Im8			0.43	0.49					2.39	0.28
Im9			0.45						1.92	0.54
Im10				0.97					1.01	0.10
Im11					0.66				1.15	0.55
Im12					1.04				1.05	0.16
Im13					0.79				1.06	0.30
Im14				0.92					1.02	0.15
Im15						0.35		0.36	2.73	0.35
Im16								1.02	1.03	0.20
Im17							0.98		1.01	0.07
Im18							0.90		1.01	0.26
Im19								0.63	1.11	0.38
Im20		0.98							1.09	0.19
Im21		0.79							1.06	0.35
Im22		0.82							1.06	0.22

7 factors: exclude 9, 15, 16, 19 6 factors: exclude 16, 17, 18, 19, 5 factors: exclude 17, 18

2.2 ROUND 2 : Exploratory factor analysis round 2

2.2.1 Variable selection for EFA

# # perform multiple variable selections
# 
# exclude <- list(c("Im1","Im2","Im16", "Im19","Im15","Im9"),
#              c("Im3","Im4","Im9", "Im15","Im11"))
# 
# survey_excl_img2 = list()
# data_img_EFA2 = list()
# 
# for (i in 1:length(exclude)){
#   survey_excl_img2[[i]] <- survey |> select(-exclude[[i]])
#   data_img_EFA2[[i]] <- survey_excl_img2[[i]][1:(22-length(exclude[[i]]))]
#   # print(survey_excl_img2[[i]])
# }
# 
# # survey_excl_img2[[1]]
# # survey_excl_img2[[2]]
# data_img_EFA2[[1]]
# data_img_EFA2[[2]]

# excluded image variables
# candidates for 7 factors: "Im9",("Im11"),"Im15", "Im19", "Im16"
# candidates for 6 factors: "Im16","Im9", "Im19", ("Im11"), ("Im15"), ("Im18"),"Im17", "Im6"

exclude=c("Im9","Im15","Im8") # "Im16", "Im19","Im9","Im11","Im15"

# the full survey data (includes dependent and independent variables) with excluded image variables
survey_excl_img2 <- survey |> select(-exclude) 

# the data we will use for EFA (images)
data_img_EFA2 <- survey_excl_img2[1:(22-length(exclude))]

The excluded variables correspond to the following:

excludedvars <- filter(labels, Variable %in% exclude)[c("Variable","Label_short")] 

excludedvars |>
  stable()

Variable	Label_short
Im8	Expertise in French Traditional Cuisine
Im9	French Fashion
Im15	Professional Selection of Brands

2.2.2 handle missing data

# delete missing data
data_img_EFA2 <- na.omit(data_img_EFA2)

dim(survey)

## [1] 553  35

dim(survey_excl_img2)

## [1] 553  32

dim(data_img_EFA2)

## [1] 394  19

2.2.3 Check adequacy of correlation Matrix

2.2.3.1 correlation matrix

#plot correlation matrix adjusting parameters to see previously identified groupings
corr_matrix <- cor(data_img_EFA2)
corrplot(as.matrix(corr_matrix), 
         method = "color", #col = c("white","white","white","white","white", "lightgrey", "darkgrey", "black"),
         order = "hclust", addrect = 10, rect.col="black", # rect.col="red",
         addCoef.col = 'black', number.cex = .5,
         tl.col ="black", 
         tl.cex = 0.80,
         )

Here we have excluded variables: Im8, Im9, Im15 corresponding to Expertise in French Traditional Cuisine, French Fashion, Professional Selection of Brands respectively

Variables to look out for going forward: - Images 9 and 11 are alone - Pairs of images: (17,18), cluster exclusively together, have a very high correlation and similar correlation profiles meaning we might only want to keep one of them. Similar comment to a lesser degree for (6,7) and (16,19).

2.2.3.2 Bartlett’s Test

bart_spher(data_img_EFA2)

##  Bartlett's Test of Sphericity
## 
## Call: bart_spher(x = data_img_EFA2)
## 
##      X2 = 5521.451
##      df = 171
## p-value < 2.22e-16

In our case we see that it is indeed rejected and that the data is not uncorrelated.

2.2.3.3 KMO

KMOTEST=KMOS(data_img_EFA2)
print(KMOTEST, sort=T)

## 
## Kaiser-Meyer-Olkin Statistics
## 
## Call: KMOS(x = data_img_EFA2)
## 
## Measures of Sampling Adequacy (MSA):
##       Im6      Im10       Im7      Im14       Im2       Im1      Im20      Im18 
## 0.7471329 0.7642565 0.7744268 0.7843674 0.7950011 0.7961197 0.8143469 0.8323628 
##       Im4      Im17      Im12       Im3      Im13      Im22      Im11      Im16 
## 0.8394241 0.8427407 0.8483413 0.8497470 0.8567410 0.8730869 0.8958364 0.9007282 
##      Im21      Im19       Im5 
## 0.9102753 0.9199391 0.9515411 
## 
## KMO-Criterion: 0.8416876

The KMO of 0.8416876 is above 0.6 which indicates the data is well suited for factor anlysis.

2.2.3.4 Anti-image Correlation

MSA_list <- data.table("Item"=names(KMOTEST$MSA), "MSA"=as.numeric(KMOTEST$MSA))

#Display table
MSA_list<- MSA_list |> 
  setorder(cols = "MSA")
  
MSA_list |> 
  stable() |> 
  row_spec(which(MSA_list[,2]<0.5), bold = T, color = "white", background = "#78BE20")

Item	MSA
Im6	0.75
Im10	0.76
Im7	0.77
Im14	0.78
Im2	0.80
Im1	0.80
Im20	0.81
Im18	0.83
Im4	0.84
Im17	0.84
Im12	0.85
Im3	0.85
Im13	0.86
Im22	0.87
Im11	0.90
Im16	0.90
Im21	0.91
Im19	0.92
Im5	0.95

Here we have excluded variables: Im8, Im9, Im15 corresponding to Expertise in French Traditional Cuisine, French Fashion, Professional Selection of Brands respectively

All variables have MSA above 0.5

2.2.4 Select method: PAF

2.2.4.1 Extract factors

EFA_PAF0 <- psych::fa(data_img_EFA2, rotate="varimax", scores=TRUE)
# note: by default number of factors = 1 if it is not specified

2.2.4.1.1 Scree plot

#display Scree-plot
plot(EFA_PAF0$e.values,xlab="Factor Number",
     ylab="Eigenvalue",
     main="Scree plot",
     cex.lab=1.2,
     cex.axis=1.2,
     cex.main=1.8,
     col = "#0099F8",
     pch = 19) 
abline(h=1, col = "#7F35B2")

Here we have excluded variables: Im8, Im9, Im15 corresponding to Expertise in French Traditional Cuisine, French Fashion, Professional Selection of Brands respectively

2.2.4.1.2 Kaiser Criterion

EFA_PAF0_kaiser_nb <- length(which(EFA_PAF0$e.values > 1))
EFA_PAF0_kaiser_nb

## [1] 6

The Kaiser criterion suggests we should retain factors with eigenvalues bigger than 1.

There are 6 factors satisfying this condition.

2.2.4.1.3 Total Variance Explained

#calculate total variance (does not change if number of factors change)
EFA_PAF0_EigenValue <- EFA_PAF0$e.values
EFA_PAF0_Variance <- EFA_PAF0_EigenValue / ncol(data_img_EFA2) * 100
EFA_PAF0_SumVariance <- cumsum(EFA_PAF0_EigenValue / ncol(data_img_EFA2))
EFA_PAF0_Total_Variance_Explained <- cbind("Factor number"=
                                            seq(1, length.out=length(EFA_PAF0_EigenValue[EFA_PAF0_EigenValue>0])),
                                          EigenValue = EFA_PAF0_EigenValue[EFA_PAF0_EigenValue>0],
                                          Variance = EFA_PAF0_Variance[EFA_PAF0_EigenValue>0],
                                          Total_Variance = EFA_PAF0_SumVariance[EFA_PAF0_EigenValue>0])
#display table
EFA_PAF0_Total_Variance_Explained |> 
  stable()

Factor number	EigenValue	Variance	Total_Variance
1	7.71	40.57	0.41
2	2.01	10.58	0.51
3	1.54	8.10	0.59
4	1.44	7.58	0.67
5	1.20	6.30	0.73
6	1.06	5.56	0.79
7	0.80	4.21	0.83
8	0.68	3.60	0.87
9	0.50	2.65	0.89
10	0.34	1.81	0.91
11	0.32	1.67	0.93
12	0.30	1.58	0.94
13	0.23	1.20	0.95
14	0.21	1.10	0.97
15	0.19	1.02	0.98
16	0.16	0.84	0.98
17	0.12	0.62	0.99
18	0.11	0.57	1.00
19	0.08	0.43	1.00

Here we have excluded variables: Im8, Im9, Im15 corresponding to Expertise in French Traditional Cuisine, French Fashion, Professional Selection of Brands respectively

With 6 factors we would explain 78.6947762% of total variance.

With 7 factors we would explain 82.9058259% of total variance.

# test eigenvalue calculation
factorloadings = EFA_PAF0$loadings[,1] # loadings 1st factor (default is nfactors = 1)
Eigenvalue = sum(factorloadings^2)
Eigenvalue

## [1] 7.109148

2.2.4.2 Determine number of factors to retain

# select nb of factors to test
nf = c(5,6,7,8)

2.2.4.3 PAF orthogonal Varimax with n factors

# perform multiple PAFs one for each factor number in selection
EFA_PAFn = list()

i=1
for (n in nf) {
  # EFA_PAFn[[i]] <- n
  EFA_PAFn[[i]] <- psych::fa(data_img_EFA2, rotate="varimax", scores=TRUE, nfactors = n)
  i=i+1
}
names(EFA_PAFn) <- nf

2.2.4.3.1 Communalities

#communalities for all selected number of factors

for (i in 1:length(nf)) {

  cat("###### Number of factors =", nf[[i]], "{.unnumbered}" ,"\n")

    EFA_PAFn_communalities <- data.table("Item"=names(EFA_PAFn[[i]]$communality), 
                             "Communality"=as.numeric(EFA_PAFn[[i]]$communality))

    # Sort table
    EFA_PAFn_communalities <- EFA_PAFn_communalities |>
      setorder(cols = "Communality")
    
    # Display table
    kbl <- EFA_PAFn_communalities |> 
              stable() |> 
              row_spec(which(EFA_PAFn_communalities[,1]<.3), bold = T, color = "white", background = "#78BE20")
    
    print(kbl)
    cat("\n\n")

    # test communality calculation
    variableloading = EFA_PAFn[[i]]$loadings["Im6",] # loadings 1st variable
    communality = sum(variableloading^2)
    print(paste0("Communality for Im6 =", communality))
    cat("\n")
    
}

Number of factors = 5

Item	Communality
Im11	0.41
Im18	0.42
Im16	0.42
Im6	0.50
Im19	0.51
Im17	0.52
Im5	0.55
Im21	0.64
Im10	0.66
Im7	0.67
Im14	0.70
Im20	0.72
Im13	0.72
Im12	0.75
Im2	0.78
Im22	0.80
Im1	0.84
Im3	0.86
Im4	0.92

[1] “Communality for Im6 =0.496673139129337”

Number of factors = 6

Item	Communality
Im16	0.42
Im11	0.45
Im19	0.51
Im5	0.55
Im6	0.64
Im21	0.64
Im18	0.65
Im13	0.69
Im10	0.71
Im7	0.73
Im12	0.74
Im14	0.74
Im20	0.78
Im22	0.79
Im2	0.80
Im17	0.83
Im3	0.86
Im1	0.89
Im4	0.92

[1] “Communality for Im6 =0.638799740882147”

Number of factors = 7

Item	Communality
Im16	0.43
Im11	0.43
Im19	0.51
Im5	0.55
Im21	0.64
Im18	0.67
Im13	0.69
Im7	0.72
Im14	0.78
Im22	0.78
Im20	0.79
Im2	0.81
Im3	0.86
Im12	0.87
Im1	0.91
Im6	0.93
Im4	0.97
Im10	0.97
Im17	1.00

[1] “Communality for Im6 =0.931925021212407”

Number of factors = 8

Item	Communality
Im11	0.43
Im5	0.58
Im21	0.64
Im16	0.67
Im18	0.68
Im13	0.69
Im7	0.69
Im19	0.70
Im2	0.76
Im14	0.78
Im22	0.78
Im20	0.81
Im3	0.86
Im12	0.87
Im4	0.97
Im6	0.99
Im10	1.00
Im17	1.00
Im1	1.00

[1] “Communality for Im6 =0.990898460352201”

Typically we should think about excluding variables with communalities below 0.3.

Based on the above, no variable should be excluded.

2.2.4.3.2 Factor loadings

# loadings for all selected number of factors

for (i in 1:length(nf)) {
  
cat("###### Number of factors =", nf[[i]], "{.unnumbered}" ,"\n")
  
      # print(EFA_PAFn[[i]]$loadings, cutoff=0.3)
      # print(print_html(model_parameters(EFA_PAFn[[i]], loadings=T, threshold = 0.3, summary=T)))
     kbl <- model_parameters(EFA_PAFn[[i]], loadings=T, threshold = 0.3, summary=T) |>
        stable()
     print(kbl)
           
cat("\n\n")
}

Number of factors = 5

Variable	MR1	MR2	MR4	MR5	MR3	Complexity	Uniqueness
Im1				0.85		1.35	0.16
Im2				0.83		1.27	0.22
Im3	0.84					1.44	0.14
Im4	0.89					1.36	0.08
Im5	0.65					1.66	0.45
Im6		0.67				1.23	0.50
Im7		0.78				1.20	0.33
Im10		0.74				1.42	0.34
Im11			0.58			1.49	0.59
Im12			0.82			1.22	0.25
Im13			0.77			1.44	0.28
Im14		0.77				1.39	0.30
Im16	0.40			0.41		3.03	0.58
Im17	0.30		0.43	0.39		3.76	0.48
Im18			0.39	0.32		3.81	0.58
Im19	0.42			0.43		3.53	0.49
Im20					0.80	1.23	0.28
Im21					0.74	1.39	0.36
Im22					0.81	1.49	0.20

Number of factors = 6

Variable	MR1	MR2	MR3	MR4	MR5	MR6	Complexity	Uniqueness
Im1					0.86		1.40	0.11
Im2					0.83		1.33	0.20
Im3	0.85						1.43	0.14
Im4	0.89						1.35	0.08
Im5	0.65						1.63	0.45
Im6		0.73					1.40	0.36
Im7		0.81					1.24	0.27
Im10		0.70		0.32			1.95	0.29
Im11				0.61			1.46	0.55
Im12				0.80			1.31	0.26
Im13				0.71			1.80	0.31
Im14		0.73		0.32			1.85	0.26
Im16	0.41				0.39		3.16	0.58
Im17						0.74	2.15	0.17
Im18						0.66	2.10	0.35
Im19	0.43				0.39		3.93	0.49
Im20			0.84				1.21	0.22
Im21			0.73				1.43	0.36
Im22			0.79				1.54	0.21

Number of factors = 7

Variable	MR1	MR3	MR4	MR5	MR2	MR6	MR7	Complexity	Uniqueness
Im1				0.87				1.40	0.09
Im2				0.83				1.35	0.19
Im3	0.84							1.46	0.14
Im4	0.92							1.33	0.03
Im5	0.64							1.73	0.45
Im6							0.93	1.17	0.07
Im7					0.33		0.75	1.62	0.28
Im10					0.92			1.32	0.03
Im11			0.57					1.70	0.57
Im12			0.88					1.23	0.13
Im13			0.72					1.76	0.31
Im14					0.77		0.30	1.67	0.22
Im16	0.38			0.37				3.99	0.57
Im17						0.88		1.60	0.00
Im18						0.70		1.84	0.33
Im19	0.40			0.37				4.52	0.49
Im20		0.85						1.19	0.21
Im21		0.73						1.43	0.36
Im22		0.79						1.55	0.22

Number of factors = 8

Variable	MR1	MR3	MR4	MR5	MR2	MR7	MR6	MR8	Complexity	Uniqueness
Im1				0.91					1.44	0.00
Im2				0.78					1.56	0.24
Im3	0.82								1.63	0.14
Im4	0.89								1.46	0.03
Im5	0.66								1.78	0.42
Im6						0.96			1.15	0.01
Im7					0.34	0.72			1.69	0.31
Im10					0.93				1.32	0.00
Im11			0.57						1.71	0.57
Im12			0.89						1.22	0.13
Im13			0.72						1.76	0.31
Im14					0.77				1.68	0.22
Im16								0.68	2.03	0.33
Im17							0.88		1.65	0.00
Im18							0.70		1.84	0.32
Im19								0.64	2.71	0.30
Im20		0.86							1.19	0.19
Im21		0.73							1.44	0.36
Im22		0.79							1.56	0.22

Here we have excluded variables: Im8, Im9, Im15 corresponding to Expertise in French Traditional Cuisine, French Fashion, Professional Selection of Brands respectively

Factor loadings:

Number of items per factor >=3
- this condition is respected in all cases except when we have 8 factors. We eliminate the 8 factor solution
0.40–0.30–0.20 rule: satisfactory variables (a) load onto their primary factor above 0.40, (b) load onto alter-native factors below 0.30, and (c) demonstrate a difference of 0.20 between their primary and alternative factor loadings.
- 5 factor solution:
  - this condition is not respected for many variables. We eliminate the 5 factor solution
- 6 factor solution:
  - this condition is not respected for: Im6, Im7, Im9, (Im11), (Im15), Im16, Im17, Im18, Im19 where Im17 and Im18 are particularly spread out
- 7 factor solution:
  - this condition is not respected for: Im7, Im8, Im9, Im15, Im16, Im19 where Im16 and Im19 are particularly spread out

Based on the above we will prefer the 7 factor solution but we will no doubt have to exclude some variables, potentially 19 as it also has the lower communality than Im16 and probably also factor 9 as it also has low communality

Thurstone simple structure criteria:

Each row (variable) of the factor pattern matrix should have at least one zero
Each column (factor) should have at least r zero elements, and the zeros for one factor should be unique from the zeros for the other factors
For every pair of columns (factors), there should be at least r variables with a zero coefficient in one column and a non-zero coefficient in the other
When r > 3 every pair of columns (factors), should contain a large proportion of variables with zeros in both columns
For every pair of columns (factors), there should be only a small proportion of variables with non-zeros in both columns

2.2.4.4 PAF oblique Promax with n factors

# perform multiple PAFs one for each factor number in selection
EFA_PAFn_obl = list()

i=1
for (n in nf) {
  # EFA_PAFn_obl[[i]] <- n
  EFA_PAFn_obl[[i]] <- psych::fa(data_img_EFA2, rotate="promax", scores=TRUE, nfactors = n)
  i=i+1
}
names(EFA_PAFn_obl) <- nf

length(EFA_PAFn_obl)

## [1] 4

2.2.4.4.1 Communalities

#communalities for all selected number of factors

for (i in 1:length(nf)) {

  cat("###### Number of factors =", nf[[i]], "{.unnumbered}" ,"\n")

    EFA_PAFn_obl_communalities <- data.table("Item"=names(EFA_PAFn_obl[[i]]$communality), 
                             "Communality"=as.numeric(EFA_PAFn_obl[[i]]$communality))

    # Sort table
    EFA_PAFn_obl_communalities <- EFA_PAFn_obl_communalities |>
      setorder(cols = "Communality")
    
    # Display table  
    kbl <- EFA_PAFn_obl_communalities |> 
              stable() |> 
              row_spec(which(EFA_PAFn_obl_communalities[,1]<.3), bold = T, color = "white", background = "#78BE20")
    
    print(kbl)
    cat("\n\n")

    # test communality calculation
    variableloading = EFA_PAFn_obl[[i]]$loadings["Im6",] # loadings 1st variable
    communality = sum(variableloading^2)
    print(paste0("Communality for Im6 =", communality))
    cat("\n")
    
}

Number of factors = 5

Item	Communality
Im11	0.41
Im18	0.42
Im16	0.42
Im6	0.50
Im19	0.51
Im17	0.52
Im5	0.55
Im21	0.64
Im10	0.66
Im7	0.67
Im14	0.70
Im20	0.72
Im13	0.72
Im12	0.75
Im2	0.78
Im22	0.80
Im1	0.84
Im3	0.86
Im4	0.92

[1] “Communality for Im6 =0.547199381232095”

Number of factors = 6

Item	Communality
Im16	0.42
Im11	0.45
Im19	0.51
Im5	0.55
Im6	0.64
Im21	0.64
Im18	0.65
Im13	0.69
Im10	0.71
Im7	0.73
Im12	0.74
Im14	0.74
Im20	0.78
Im22	0.79
Im2	0.80
Im17	0.83
Im3	0.86
Im1	0.89
Im4	0.92

[1] “Communality for Im6 =0.833006250441541”

Number of factors = 7

Item	Communality
Im16	0.43
Im11	0.43
Im19	0.51
Im5	0.55
Im21	0.64
Im18	0.67
Im13	0.69
Im7	0.72
Im14	0.78
Im22	0.78
Im20	0.79
Im2	0.81
Im3	0.86
Im12	0.87
Im1	0.91
Im6	0.93
Im4	0.97
Im10	0.97
Im17	1.00

[1] “Communality for Im6 =0.971113915290573”

Number of factors = 8

Item	Communality
Im11	0.43
Im5	0.58
Im21	0.64
Im16	0.67
Im18	0.68
Im13	0.69
Im7	0.69
Im19	0.70
Im2	0.76
Im14	0.78
Im22	0.78
Im20	0.81
Im3	0.86
Im12	0.87
Im4	0.97
Im6	0.99
Im10	1.00
Im17	1.00
Im1	1.00

[1] “Communality for Im6 =1.14058133882705”

2.2.4.4.2 Factor loadings

# loadings for all selected number of factors

test = list()

for (i in 1:length(nf)) {
  
cat("###### Number of factors =", nf[[i]], "{.unnumbered}" ,"\n")
  
      # print(EFA_PAFn_obl[[i]]$loadings, cutoff=0.3)
      # print(print_html(model_parameters(EFA_PAFn_obl[[i]], loadings=T, threshold = 0.3, summary=T)))
     kbl <- model_parameters(EFA_PAFn_obl[[i]], loadings=T, threshold = 0.3, summary=T) |>
        stable()
     print(kbl)
      
cat("\n\n")
}

Number of factors = 5

Variable	MR1	MR2	MR5	MR4	MR3	Complexity	Uniqueness
Im1			1.06			1.05	0.16
Im2			1.06			1.07	0.22
Im3	1.05					1.04	0.14
Im4	1.11					1.05	0.08
Im5	0.77					1.03	0.45
Im6		0.72				1.12	0.50
Im7		0.85				1.15	0.33
Im10		0.75				1.21	0.34
Im11				0.68		1.09	0.59
Im12				1.00		1.04	0.25
Im13				0.89		1.02	0.28
Im14		0.78				1.14	0.30
Im16	0.33		0.36			2.14	0.58
Im17				0.34		2.56	0.48
Im18				0.31		2.71	0.58
Im19	0.32		0.36			2.28	0.49
Im20					0.88	1.07	0.28
Im21					0.78	1.06	0.36
Im22					0.84	1.02	0.20

Number of factors = 6

Variable	MR1	MR2	MR3	MR5	MR4	MR6	Complexity	Uniqueness
Im1				1.04			1.05	0.11
Im2				1.00			1.04	0.20
Im3	1.02						1.05	0.14
Im4	1.08						1.05	0.08
Im5	0.76						1.03	0.45
Im6		0.84					1.39	0.36
Im7		0.91					1.18	0.27
Im10		0.68					1.69	0.29
Im11					0.67		1.05	0.55
Im12					0.91		1.06	0.26
Im13					0.77		1.22	0.31
Im14		0.71					1.55	0.26
Im16	0.33			0.33			2.12	0.58
Im17						0.77	1.14	0.17
Im18						0.69	1.14	0.35
Im19	0.33						2.58	0.49
Im20			0.91				1.08	0.22
Im21			0.75				1.06	0.36
Im22			0.80				1.04	0.21

Number of factors = 7

Variable	MR1	MR3	MR5	MR4	MR2	MR6	MR7	Complexity	Uniqueness
Im1			1.07					1.05	0.09
Im2			1.02					1.03	0.19
Im3	1.01							1.02	0.14
Im4	1.14							1.05	0.03
Im5	0.73							1.02	0.45
Im6							0.98	1.04	0.07
Im7							0.73	1.16	0.28
Im10					1.10			1.03	0.03
Im11				0.60				1.16	0.57
Im12				1.00				1.03	0.13
Im13				0.75				1.11	0.31
Im14					0.87			1.04	0.22
Im16								3.60	0.57
Im17						1.12		1.02	0.00
Im18						0.86		1.03	0.33
Im19								3.47	0.49
Im20		0.94						1.04	0.21
Im21		0.77						1.05	0.36
Im22		0.82						1.03	0.22

Number of factors = 8

Variable	MR1	MR3	MR4	MR2	MR5	MR6	MR7	MR8	Complexity	Uniqueness
Im1					1.03				1.01	0.00
Im2					0.86				1.01	0.24
Im3	0.90								1.02	0.14
Im4	1.02								1.03	0.03
Im5	0.73								1.09	0.42
Im6							1.06		1.03	0.01
Im7							0.72		1.14	0.31
Im10				1.05					1.02	0.00
Im11			0.60						1.15	0.57
Im12			1.02						1.04	0.13
Im13			0.75						1.09	0.31
Im14				0.82					1.03	0.22
Im16								0.80	1.02	0.33
Im17						1.03			1.01	0.00
Im18						0.81			1.00	0.32
Im19								0.72	1.04	0.30
Im20		0.97							1.09	0.19
Im21		0.77							1.05	0.36
Im22		0.82							1.04	0.22

Here we have excluded variables: Im8, Im9, Im15 corresponding to Expertise in French Traditional Cuisine, French Fashion, Professional Selection of Brands respectively

2.3 Confirmatory factor analysis

We test whether the constructs found in the exploratory phase adequately describe what is going on.

2.3.1 6 factor model

# no excluded variables
CFA_model_img_6f <- "
DECO =~ Im3 + Im4 + Im5
FRENCH =~ Im6 + Im7 + Im8 + Im10 + Im14
ATMOS =~ Im20 + Im21 + Im22
QUAL =~ Im11 + Im12 + Im13
CHOICE =~ Im1 + Im2 + Im15 + Im16 + Im19
BRAND =~ Im17 + Im18 + Im9
"

# # excluded variables: Im9, Im15, Im16, Im19
# CFA_model_img_6f <- "
# QUAL =~ Im11 + Im12 + Im13
# FRENCH =~ Im6 + Im7 + Im8 + Im10 + Im14
# ATMOS =~ Im20 + Im21 + Im22
# DECO =~ Im3 + Im4 + Im5
# CHOICE =~ Im1 + Im2
# BRAND =~ Im17 + Im18
# "

# # excluded variables: Im9, Im15, Im16, Im19, Im8
# CFA_model_img_6f <- "
# QUAL =~ Im11 + Im12 + Im13
# FRENCH =~ Im6 + Im7 + Im10 + Im14
# ATMOS =~ Im20 + Im21 + Im22
# DECO =~ Im3 + Im4 + Im5
# CHOICE =~ Im1 + Im2
# BRAND =~ Im17 + Im18
# "

# CFA_fit_img <- cfa(CFA_model_img_6f, data=data_img_EFA, missing="ML")
CFA_fit_img_6f <- cfa(CFA_model_img_6f, data=survey, missing="ML")

summary(CFA_fit_img_6f, fit.measures=TRUE, standardized=TRUE)

## lavaan 0.6.15 ended normally after 110 iterations
## 
##   Estimator                                         ML
##   Optimization method                           NLMINB
##   Number of model parameters                        81
## 
##   Number of observations                           553
##   Number of missing patterns                        87
## 
## Model Test User Model:
##                                                       
##   Test statistic                              1442.584
##   Degrees of freedom                               194
##   P-value (Chi-square)                           0.000
## 
## Model Test Baseline Model:
## 
##   Test statistic                              8838.959
##   Degrees of freedom                               231
##   P-value                                        0.000
## 
## User Model versus Baseline Model:
## 
##   Comparative Fit Index (CFI)                    0.855
##   Tucker-Lewis Index (TLI)                       0.827
##                                                       
##   Robust Comparative Fit Index (CFI)             0.854
##   Robust Tucker-Lewis Index (TLI)                0.827
## 
## Loglikelihood and Information Criteria:
## 
##   Loglikelihood user model (H0)             -15479.697
##   Loglikelihood unrestricted model (H1)     -14758.405
##                                                       
##   Akaike (AIC)                               31121.394
##   Bayesian (BIC)                             31470.938
##   Sample-size adjusted Bayesian (SABIC)      31213.808
## 
## Root Mean Square Error of Approximation:
## 
##   RMSEA                                          0.108
##   90 Percent confidence interval - lower         0.103
##   90 Percent confidence interval - upper         0.113
##   P-value H_0: RMSEA <= 0.050                    0.000
##   P-value H_0: RMSEA >= 0.080                    1.000
##                                                       
##   Robust RMSEA                                   0.110
##   90 Percent confidence interval - lower         0.105
##   90 Percent confidence interval - upper         0.116
##   P-value H_0: Robust RMSEA <= 0.050             0.000
##   P-value H_0: Robust RMSEA >= 0.080             1.000
## 
## Standardized Root Mean Square Residual:
## 
##   SRMR                                           0.092
## 
## Parameter Estimates:
## 
##   Standard errors                             Standard
##   Information                                 Observed
##   Observed information based on                Hessian
## 
## Latent Variables:
##                    Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
##   DECO =~                                                               
##     Im3               1.000                               1.236    0.936
##     Im4               1.057    0.025   42.551    0.000    1.307    0.970
##     Im5               0.820    0.034   23.857    0.000    1.013    0.761
##   FRENCH =~                                                             
##     Im6               1.000                               0.642    0.535
##     Im7               1.219    0.106   11.525    0.000    0.783    0.644
##     Im8               1.244    0.099   12.567    0.000    0.799    0.755
##     Im10              1.251    0.095   13.133    0.000    0.803    0.914
##     Im14              1.244    0.095   13.142    0.000    0.799    0.929
##   ATMOS =~                                                              
##     Im20              1.000                               1.268    0.848
##     Im21              0.848    0.041   20.879    0.000    1.075    0.785
##     Im22              1.053    0.046   22.697    0.000    1.335    0.873
##   QUAL =~                                                               
##     Im11              1.000                               0.703    0.615
##     Im12              1.410    0.094   15.050    0.000    0.991    0.872
##     Im13              1.465    0.105   13.982    0.000    1.030    0.855
##   CHOICE =~                                                             
##     Im1               1.000                               1.232    0.926
##     Im2               0.942    0.027   34.780    0.000    1.160    0.902
##     Im15              0.720    0.036   20.097    0.000    0.887    0.740
##     Im16              0.567    0.041   13.849    0.000    0.699    0.579
##     Im19              0.540    0.038   14.310    0.000    0.666    0.592
##   BRAND =~                                                              
##     Im17              1.000                               1.184    0.952
##     Im18              1.025    0.038   27.280    0.000    1.214    0.868
##     Im9               0.540    0.047   11.386    0.000    0.640    0.474
## 
## Covariances:
##                    Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
##   DECO ~~                                                               
##     FRENCH            0.344    0.046    7.416    0.000    0.434    0.434
##     ATMOS             0.730    0.082    8.901    0.000    0.466    0.466
##     QUAL              0.409    0.051    8.040    0.000    0.471    0.471
##     CHOICE            0.782    0.079    9.940    0.000    0.514    0.514
##     BRAND             0.778    0.076   10.268    0.000    0.531    0.531
##   FRENCH ~~                                                             
##     ATMOS             0.265    0.045    5.888    0.000    0.326    0.326
##     QUAL              0.206    0.030    6.812    0.000    0.456    0.456
##     CHOICE            0.299    0.044    6.737    0.000    0.378    0.378
##     BRAND             0.277    0.042    6.547    0.000    0.364    0.364
##   ATMOS ~~                                                              
##     QUAL              0.373    0.053    7.021    0.000    0.419    0.419
##     CHOICE            0.767    0.083    9.216    0.000    0.491    0.491
##     BRAND             0.792    0.081    9.797    0.000    0.528    0.528
##   QUAL ~~                                                               
##     CHOICE            0.460    0.054    8.585    0.000    0.531    0.531
##     BRAND             0.483    0.053    9.113    0.000    0.581    0.581
##   CHOICE ~~                                                             
##     BRAND             0.864    0.078   11.040    0.000    0.592    0.592
## 
## Intercepts:
##                    Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
##    .Im3               4.994    0.056   88.528    0.000    4.994    3.785
##    .Im4               4.997    0.057   86.919    0.000    4.997    3.709
##    .Im5               5.034    0.057   87.796    0.000    5.034    3.785
##    .Im6               5.824    0.051  113.338    0.000    5.824    4.849
##    .Im7               5.751    0.053  109.497    0.000    5.751    4.727
##    .Im8               6.000    0.045  133.008    0.000    6.000    5.671
##    .Im10              6.100    0.037  163.041    0.000    6.100    6.945
##    .Im14              6.139    0.037  166.909    0.000    6.139    7.138
##    .Im20              4.672    0.064   73.182    0.000    4.672    3.124
##    .Im21              5.139    0.058   87.973    0.000    5.139    3.751
##    .Im22              4.278    0.065   65.391    0.000    4.278    2.798
##    .Im11              5.653    0.049  115.277    0.000    5.653    4.943
##    .Im12              5.666    0.049  116.095    0.000    5.666    4.983
##    .Im13              5.448    0.052  105.630    0.000    5.448    4.525
##    .Im1               4.792    0.057   84.316    0.000    4.792    3.601
##    .Im2               4.861    0.055   88.357    0.000    4.861    3.779
##    .Im15              5.090    0.051   99.219    0.000    5.090    4.246
##    .Im16              5.130    0.052   98.387    0.000    5.130    4.251
##    .Im19              5.146    0.048  106.829    0.000    5.146    4.578
##    .Im17              5.025    0.053   94.490    0.000    5.025    4.038
##    .Im18              4.595    0.060   76.460    0.000    4.595    3.286
##    .Im9               5.075    0.058   87.318    0.000    5.075    3.757
##     DECO              0.000                               0.000    0.000
##     FRENCH            0.000                               0.000    0.000
##     ATMOS             0.000                               0.000    0.000
##     QUAL              0.000                               0.000    0.000
##     CHOICE            0.000                               0.000    0.000
##     BRAND             0.000                               0.000    0.000
## 
## Variances:
##                    Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
##    .Im3               0.215    0.024    8.776    0.000    0.215    0.123
##    .Im4               0.108    0.024    4.439    0.000    0.108    0.060
##    .Im5               0.744    0.049   15.192    0.000    0.744    0.421
##    .Im6               1.030    0.066   15.665    0.000    1.030    0.714
##    .Im7               0.867    0.059   14.739    0.000    0.867    0.586
##    .Im8               0.482    0.034   14.159    0.000    0.482    0.430
##    .Im10              0.127    0.013    9.840    0.000    0.127    0.164
##    .Im14              0.101    0.012    8.329    0.000    0.101    0.137
##    .Im20              0.629    0.061   10.379    0.000    0.629    0.281
##    .Im21              0.721    0.057   12.668    0.000    0.721    0.384
##    .Im22              0.554    0.063    8.781    0.000    0.554    0.237
##    .Im11              0.814    0.055   14.805    0.000    0.814    0.622
##    .Im12              0.310    0.039    7.857    0.000    0.310    0.240
##    .Im13              0.390    0.044    8.777    0.000    0.390    0.269
##    .Im1               0.253    0.035    7.312    0.000    0.253    0.143
##    .Im2               0.308    0.033    9.422    0.000    0.308    0.186
##    .Im15              0.651    0.048   13.673    0.000    0.651    0.453
##    .Im16              0.968    0.065   14.927    0.000    0.968    0.664
##    .Im19              0.820    0.055   14.954    0.000    0.820    0.649
##    .Im17              0.146    0.036    4.039    0.000    0.146    0.094
##    .Im18              0.482    0.046   10.494    0.000    0.482    0.247
##    .Im9               1.415    0.089   15.908    0.000    1.415    0.776
##     DECO              1.527    0.107   14.308    0.000    1.000    1.000
##     FRENCH            0.412    0.064    6.422    0.000    1.000    1.000
##     ATMOS             1.608    0.138   11.683    0.000    1.000    1.000
##     QUAL              0.494    0.067    7.365    0.000    1.000    1.000
##     CHOICE            1.518    0.110   13.746    0.000    1.000    1.000
##     BRAND             1.402    0.100   14.036    0.000    1.000    1.000

2.3.1.1 Discussion of global fit measures

Chi square: p-value > 0.05

RMSEA RMSEA <= 0.05 Good fit 0.05 < RMSEA <= 0.08 Acceptable fit 0.08 < RMSEA <= 0.10 Bad fit RMSEA > 0.1 Unacceptable fit

CFI CFI < 0.90 definitely reject model 0.90 < CFI < 0.95 high underrejection rates for misspecified models CFI > 0.95 accept model

2.3.1.2 local fit measures

# semPaths(CFA_fit_img_6f, what = "path", whatLabels = "std", style = "mx",
#          rotation = 2, layout = "tree3", mar = c(1, 2, 1, 2), 
#          nCharNodes = 7,shapeMan = "rectangle", sizeMan = 8, sizeMan2 = 5, 
#          curvePivot=TRUE, edge.label.cex = 1.2, edge.color = "skyblue4")


semPaths(CFA_fit_img_6f, what = "path", whatLabels = "std", style = "mx",
         rotation = 2, layout = "tree3", mar = c(1, 2, 1, 2), 
         nCharNodes = 7,shapeMan = "rectangle", 
         sizeMan = 4, sizeMan2 = 3, sizeInt = 2, sizeLat = 6, asize = 1.5,
         curvePivot=TRUE, edge.label.cex = .8, edge.color = "skyblue4"
         )

lambda = inspect(CFA_fit_img_6f, what="std")$lambda
theta = inspect(CFA_fit_img_6f, what="std")$theta

# create lambda matrix with ones instead of std.all
ones <- lambda
ones[ones>0] <- 1

# a matrix with dimensions of lambda matrix but with lambdas replaced by thetas
theta_lb <- theta %*% ones

2.3.1.2.1 Indicator reliability criterion (Individual Item Reliability)

# JONATHAN
# calculate indicator reliabilities (should be larger than 0.4)
indicrel <- lambda^2/(lambda^2 + theta_lb)
# indicrel

# replace all values satisfying condition with NaN for visibility
indicrel_fail <- indicrel
indicrel_fail[indicrel_fail>.4] <- NaN
indicrel_fail

##      DECO FRENCH ATMOS  QUAL CHOICE BRAND
## Im3   NaN    NaN   NaN   NaN    NaN   NaN
## Im4   NaN    NaN   NaN   NaN    NaN   NaN
## Im5   NaN    NaN   NaN   NaN    NaN   NaN
## Im6   NaN  0.286   NaN   NaN    NaN   NaN
## Im7   NaN    NaN   NaN   NaN    NaN   NaN
## Im8   NaN    NaN   NaN   NaN    NaN   NaN
## Im10  NaN    NaN   NaN   NaN    NaN   NaN
## Im14  NaN    NaN   NaN   NaN    NaN   NaN
## Im20  NaN    NaN   NaN   NaN    NaN   NaN
## Im21  NaN    NaN   NaN   NaN    NaN   NaN
## Im22  NaN    NaN   NaN   NaN    NaN   NaN
## Im11  NaN    NaN   NaN 0.378    NaN   NaN
## Im12  NaN    NaN   NaN   NaN    NaN   NaN
## Im13  NaN    NaN   NaN   NaN    NaN   NaN
## Im1   NaN    NaN   NaN   NaN    NaN   NaN
## Im2   NaN    NaN   NaN   NaN    NaN   NaN
## Im15  NaN    NaN   NaN   NaN    NaN   NaN
## Im16  NaN    NaN   NaN   NaN  0.336   NaN
## Im19  NaN    NaN   NaN   NaN  0.351   NaN
## Im17  NaN    NaN   NaN   NaN    NaN   NaN
## Im18  NaN    NaN   NaN   NaN    NaN   NaN
## Im9   NaN    NaN   NaN   NaN    NaN 0.224

# FERESHTEH
#Local Fit

std.loadings<- inspect(CFA_fit_img_6f, what="std")$lambda
check=std.loadings
check[check>0] <- 1
std.loadings[std.loadings==0] <- NA
std.loadings2 <- std.loadings^2
std.theta<- inspect(CFA_fit_img_6f, what="std")$theta

#Individual item Reliability
IIR=std.loadings2/(colSums(std.theta)+std.loadings2)
IIR

##       DECO FRENCH ATMOS  QUAL CHOICE BRAND
## Im3  0.877     NA    NA    NA     NA    NA
## Im4  0.940     NA    NA    NA     NA    NA
## Im5  0.579     NA    NA    NA     NA    NA
## Im6     NA  0.286    NA    NA     NA    NA
## Im7     NA  0.414    NA    NA     NA    NA
## Im8     NA  0.570    NA    NA     NA    NA
## Im10    NA  0.836    NA    NA     NA    NA
## Im14    NA  0.863    NA    NA     NA    NA
## Im20    NA     NA 0.719    NA     NA    NA
## Im21    NA     NA 0.616    NA     NA    NA
## Im22    NA     NA 0.763    NA     NA    NA
## Im11    NA     NA    NA 0.378     NA    NA
## Im12    NA     NA    NA 0.760     NA    NA
## Im13    NA     NA    NA 0.731     NA    NA
## Im1     NA     NA    NA    NA  0.857    NA
## Im2     NA     NA    NA    NA  0.814    NA
## Im15    NA     NA    NA    NA  0.547    NA
## Im16    NA     NA    NA    NA  0.336    NA
## Im19    NA     NA    NA    NA  0.351    NA
## Im17    NA     NA    NA    NA     NA 0.906
## Im18    NA     NA    NA    NA     NA 0.753
## Im9     NA     NA    NA    NA     NA 0.224

2.3.1.2.2 Construct reliability criterion

# JONATHAN
# calculate construct reliability (should be above .6)
constrrel <- (t(lambda) %*% ones)^2 / ((t(lambda) %*% ones)^2 + t(theta_lb) %*% ones )
# constrrel

# replace all values satisfying condition with NaN for visibility
constrrel_fail <- constrrel
constrrel_fail[constrrel_fail>.6] <- NaN
constrrel_fail

##        DECO FRENCH ATMOS QUAL CHOICE BRAND
## DECO    NaN    NaN   NaN  NaN    NaN   NaN
## FRENCH  NaN    NaN   NaN  NaN    NaN   NaN
## ATMOS   NaN    NaN   NaN  NaN    NaN   NaN
## QUAL    NaN    NaN   NaN  NaN    NaN   NaN
## CHOICE  NaN    NaN   NaN  NaN    NaN   NaN
## BRAND   NaN    NaN   NaN  NaN    NaN   NaN

# FERESHTEH
#Composite/Construct Reliability
sum.std.loadings<-colSums(std.loadings, na.rm=TRUE)^2
sum.std.theta<-rowSums(std.theta)
sum.std.theta=check*sum.std.theta
CR=sum.std.loadings/(sum.std.loadings+colSums(sum.std.theta))
CR

##      DECO    FRENCH     ATMOS      QUAL    CHOICE     BRAND 
## 0.9218076 0.8753546 0.8744065 0.8289549 0.8696442 0.8248951

2.3.1.2.3 Average Variance Extracted criterion

# JONATHAN
# calculate Average Variance Extracted (should be above .5)
AVE <- (t(lambda) %*% lambda) / (t(lambda) %*% lambda + t(theta_lb) %*% ones )
# avgvar

# replace all values satisfying condition with NaN for visibility
AVE_fail <- AVE
AVE_fail[AVE_fail>.5] <- NaN
AVE_fail

##        DECO FRENCH ATMOS QUAL CHOICE BRAND
## DECO    NaN    NaN   NaN  NaN    NaN   NaN
## FRENCH  NaN    NaN   NaN  NaN    NaN   NaN
## ATMOS   NaN    NaN   NaN  NaN    NaN   NaN
## QUAL    NaN    NaN   NaN  NaN    NaN   NaN
## CHOICE  NaN    NaN   NaN  NaN    NaN   NaN
## BRAND   NaN    NaN   NaN  NaN    NaN   NaN

# FERESHTEH
#Average Variance Extracted 
std.loadings<- inspect(CFA_fit_img_6f, what="std")$lambda
std.loadings <- std.loadings^2
AVE_fshteh=colSums(std.loadings)/(colSums(sum.std.theta)+colSums(std.loadings))
AVE_fshteh

##      DECO    FRENCH     ATMOS      QUAL    CHOICE     BRAND 
## 0.7988422 0.5938271 0.6992777 0.6229362 0.5808676 0.6278343

2.3.1.2.4 Fornell-Larcker Criteria

# JONATHAN
# correlations between constructs (factors...) should be lower than .7
psi = inspect(CFA_fit_img_6f, what="std")$psi
psi_fail <- psi
psi_fail[psi_fail<.7] <- NaN
psi_fail

##        DECO FRENCH ATMOS QUAL CHOICE BRAND
## DECO      1                               
## FRENCH  NaN      1                        
## ATMOS   NaN    NaN     1                  
## QUAL    NaN    NaN   NaN    1             
## CHOICE  NaN    NaN   NaN  NaN      1      
## BRAND   NaN    NaN   NaN  NaN    NaN     1

# JONATHAN
# AVE should be higher than squared correlations between constructs

#psi matrix squared
psi2 <- psi^2

# replace diagonal of psi matrix with AVE values
psi2 <- psi2 - psi2 * diag(1,nrow(psi2),ncol(psi2)) + diag(AVE) * diag(1,nrow(AVE),ncol(AVE))

# create matrix with columns filled with AVE
AVE_full <- AVE
AVE_full[is.na(AVE_full)] <- 0 #replace NAs with 0s
AVE_full <- AVE_full^0 %*% AVE_full # multiply a matrix full of ones with AVE_full to get columns filled with AVE

# substract matrices any psi bigger than AVE will be negative
AVEpsi_fail <- AVE_full - psi2
# AVE_full - psi2
AVEpsi_fail[AVEpsi_fail >= 0] <- NaN

AVE_full

##             DECO    FRENCH     ATMOS      QUAL    CHOICE     BRAND
## DECO   0.7988422 0.5938271 0.6992777 0.6229362 0.5808676 0.6278343
## FRENCH 0.7988422 0.5938271 0.6992777 0.6229362 0.5808676 0.6278343
## ATMOS  0.7988422 0.5938271 0.6992777 0.6229362 0.5808676 0.6278343
## QUAL   0.7988422 0.5938271 0.6992777 0.6229362 0.5808676 0.6278343
## CHOICE 0.7988422 0.5938271 0.6992777 0.6229362 0.5808676 0.6278343
## BRAND  0.7988422 0.5938271 0.6992777 0.6229362 0.5808676 0.6278343

psi2

##         DECO FRENCH ATMOS  QUAL CHOICE BRAND
## DECO   0.799                                
## FRENCH 0.188  0.594                         
## ATMOS  0.217  0.106 0.699                   
## QUAL   0.222  0.208 0.175 0.623             
## CHOICE 0.264  0.143 0.241 0.282  0.581      
## BRAND  0.282  0.132 0.279 0.337  0.350 0.628

AVEpsi_fail

##          DECO FRENCH  ATMOS   QUAL CHOICE  BRAND
## DECO        .                                   
## FRENCH    NaN      .                            
## ATMOS     NaN    NaN      .                     
## QUAL      NaN    NaN    NaN      .              
## CHOICE    NaN    NaN    NaN    NaN      .       
## BRAND     NaN    NaN    NaN    NaN    NaN      .

# FERESHTEH
std_fit1=inspect(CFA_fit_img_6f, "std")
std_fit1$psi^2

##         DECO FRENCH ATMOS  QUAL CHOICE BRAND
## DECO   1.000                                
## FRENCH 0.188  1.000                         
## ATMOS  0.217  0.106 1.000                   
## QUAL   0.222  0.208 0.175 1.000             
## CHOICE 0.264  0.143 0.241 0.282  1.000      
## BRAND  0.282  0.132 0.279 0.337  0.350 1.000

2.3.1.3 Modification indices

arrange(modificationindices(CFA_fit_img_6f),-mi)

##        lhs op  rhs      mi    epc sepc.lv sepc.all sepc.nox
## 1      Im1 ~~  Im2 495.934  0.951   0.951    3.408    3.408
## 2     Im10 ~~ Im14 298.631  0.357   0.357    3.154    3.154
## 3      Im6 ~~  Im7 255.917  0.693   0.693    0.734    0.734
## 4     Im16 ~~ Im19 128.231  0.463   0.463    0.519    0.519
## 5      Im7 ~~  Im8 104.366  0.316   0.316    0.489    0.489
## 6     DECO =~ Im19  76.462  0.344   0.424    0.378    0.378
## 7   FRENCH =~  Im9  73.482  0.783   0.503    0.372    0.372
## 8      Im6 ~~ Im10  55.895 -0.158  -0.158   -0.438   -0.438
## 9      Im1 ~~ Im16  55.410 -0.242  -0.242   -0.489   -0.489
## 10    QUAL =~ Im15  54.596  0.510   0.359    0.299    0.299
## 11     Im6 ~~  Im8  52.130  0.236   0.236    0.335    0.335
## 12     Im7 ~~ Im14  50.063 -0.145  -0.145   -0.491   -0.491
## 13  FRENCH =~ Im19  49.872  0.497   0.319    0.284    0.284
## 14    Im15 ~~ Im16  49.062  0.263   0.263    0.332    0.332
## 15     Im1 ~~ Im19  46.763 -0.204  -0.204   -0.449   -0.449
## 16    QUAL =~  Im9  45.834  0.702   0.494    0.365    0.365
## 17     Im2 ~~ Im19  45.384 -0.198  -0.198   -0.393   -0.393
## 18     Im7 ~~  Im9  45.214  0.340   0.340    0.307    0.307
## 19    DECO =~ Im16  44.633  0.288   0.356    0.295    0.295
## 20   BRAND =~ Im19  43.739  0.300   0.355    0.316    0.316
## 21     Im7 ~~ Im10  41.088 -0.134  -0.134   -0.406   -0.406
## 22    QUAL =~  Im2  38.006 -0.361  -0.254   -0.197   -0.197
## 23   BRAND =~ Im15  37.135  0.254   0.301    0.251    0.251
## 24    Im17 ~~ Im18  36.588  0.762   0.762    2.870    2.870
## 25     Im2 ~~ Im15  35.103 -0.179  -0.179   -0.399   -0.399
## 26    Im15 ~~ Im19  34.736  0.202   0.202    0.277    0.277
## 27    QUAL =~ Im19  33.294  0.434   0.305    0.271    0.271
## 28     Im8 ~~ Im14  32.038 -0.103  -0.103   -0.467   -0.467
## 29     Im6 ~~  Im9  31.342  0.301   0.301    0.249    0.249
## 30     Im1 ~~ Im15  30.586 -0.174  -0.174   -0.429   -0.429
## 31     Im2 ~~ Im16  28.333 -0.170  -0.170   -0.311   -0.311
## 32    DECO =~ Im15  27.803  0.191   0.236    0.197    0.197
## 33     Im6 ~~ Im14  27.360 -0.108  -0.108   -0.335   -0.335
## 34  FRENCH =~ Im16  27.263  0.403   0.259    0.214    0.214
## 35    DECO =~  Im2  26.666 -0.158  -0.195   -0.152   -0.152
## 36   ATMOS =~ Im15  24.669  0.181   0.230    0.192    0.192
## 37   BRAND =~ Im13  23.589  0.232   0.275    0.228    0.228
## 38    DECO =~  Im1  22.892 -0.149  -0.184   -0.138   -0.138
## 39   ATMOS =~  Im2  21.308 -0.142  -0.180   -0.140   -0.140
## 40    Im11 ~~ Im13  21.300 -0.191  -0.191   -0.339   -0.339
## 41   BRAND =~  Im2  21.047 -0.165  -0.195   -0.152   -0.152
## 42  FRENCH =~  Im1  20.125 -0.244  -0.156   -0.118   -0.118
## 43  FRENCH =~ Im15  18.582  0.279   0.179    0.149    0.149
## 44   BRAND =~ Im12  18.526 -0.197  -0.233   -0.205   -0.205
## 45   BRAND =~ Im16  17.630  0.209   0.247    0.205    0.205
## 46   BRAND =~  Im1  16.671 -0.150  -0.177   -0.133   -0.133
## 47   ATMOS =~ Im19  16.384  0.161   0.204    0.181    0.181
## 48   BRAND =~  Im6  14.589  0.161   0.191    0.159    0.159
## 49  CHOICE =~ Im20  14.430 -0.169  -0.208   -0.139   -0.139
## 50    Im14 ~~  Im9  13.864 -0.082  -0.082   -0.217   -0.217
## 51    Im11 ~~ Im12  13.374  0.145   0.145    0.289    0.289
## 52    Im21 ~~ Im22  13.217 -0.270  -0.270   -0.427   -0.427
## 53  CHOICE =~ Im13  13.044  0.152   0.187    0.155    0.155
## 54   ATMOS =~  Im7  12.806  0.134   0.170    0.140    0.140
## 55     Im8 ~~ Im10  12.666 -0.065  -0.065   -0.265   -0.265
## 56  FRENCH =~ Im11  12.345  0.269   0.173    0.151    0.151
## 57  CHOICE =~ Im12  11.541 -0.136  -0.168   -0.148   -0.148
## 58     Im3 ~~  Im4  11.447  0.264   0.264    1.735    1.735
## 59   ATMOS =~ Im16  11.243  0.146   0.185    0.153    0.153
## 60   ATMOS =~ Im12  11.072 -0.115  -0.146   -0.128   -0.128
## 61     Im8 ~~  Im9  10.943  0.125   0.125    0.152    0.152
## 62  FRENCH =~  Im2  10.891 -0.177  -0.114   -0.088   -0.088
## 63     Im7 ~~ Im22  10.253  0.126   0.126    0.182    0.182
## 64    DECO =~  Im9  10.194  0.167   0.207    0.153    0.153
## 65    Im11 ~~  Im9  10.067  0.156   0.156    0.145    0.145
## 66    Im15 ~~  Im9   9.926  0.139   0.139    0.145    0.145
## 67    QUAL =~ Im16   9.231  0.250   0.176    0.146    0.146
## 68     Im8 ~~ Im15   9.159  0.080   0.080    0.144    0.144
## 69   ATMOS =~  Im9   9.070  0.162   0.205    0.152    0.152
## 70    Im13 ~~ Im17   9.051  0.067   0.067    0.281    0.281
## 71     Im6 ~~ Im22   8.985  0.125   0.125    0.166    0.166
## 72    Im20 ~~ Im21   8.930  0.206   0.206    0.306    0.306
## 73   BRAND =~ Im22   8.880  0.147   0.175    0.114    0.114
## 74     Im8 ~~ Im16   8.801  0.095   0.095    0.139    0.139
## 75   BRAND =~ Im20   8.486 -0.141  -0.167   -0.111   -0.111
## 76   BRAND =~  Im7   8.244  0.114   0.135    0.111    0.111
## 77     Im3 ~~  Im1   8.143 -0.045  -0.045   -0.194   -0.194
## 78     Im8 ~~  Im2   7.823 -0.059  -0.059   -0.153   -0.153
## 79    QUAL =~ Im18   7.388 -0.230  -0.161   -0.115   -0.115
## 80    Im10 ~~ Im16   7.338  0.052   0.052    0.149    0.149
## 81    Im13 ~~  Im1   7.263  0.060   0.060    0.191    0.191
## 82     Im4 ~~ Im17   7.109 -0.041  -0.041   -0.322   -0.322
## 83    Im22 ~~ Im12   7.028 -0.078  -0.078   -0.189   -0.189
## 84    Im17 ~~  Im9   7.005 -0.112  -0.112   -0.247   -0.247
## 85    DECO =~  Im6   6.969  0.109   0.134    0.112    0.112
## 86   ATMOS =~ Im11   6.857  0.102   0.130    0.113    0.113
## 87  CHOICE =~  Im9   6.692  0.148   0.182    0.135    0.135
## 88   ATMOS =~  Im6   6.616  0.102   0.130    0.108    0.108
## 89    Im14 ~~  Im2   6.285  0.031   0.031    0.175    0.175
## 90   BRAND =~  Im5   6.246  0.103   0.122    0.092    0.092
## 91   BRAND =~  Im4   6.180 -0.071  -0.084   -0.062   -0.062
## 92    Im22 ~~  Im9   5.999  0.121   0.121    0.136    0.136
## 93    QUAL =~  Im5   5.978  0.169   0.119    0.089    0.089
## 94     Im1 ~~  Im9   5.822 -0.084  -0.084   -0.140   -0.140
## 95    QUAL =~  Im1   5.747 -0.143  -0.100   -0.075   -0.075
## 96  CHOICE =~ Im18   5.737 -0.115  -0.141   -0.101   -0.101
## 97     Im3 ~~  Im5   5.693 -0.084  -0.084   -0.209   -0.209
## 98     Im8 ~~ Im22   5.661  0.070   0.070    0.136    0.136
## 99    DECO =~ Im20   5.578 -0.100  -0.123   -0.082   -0.082
## 100  ATMOS =~  Im5   5.473  0.089   0.112    0.084    0.084
## 101   DECO =~ Im17   5.404 -0.091  -0.112   -0.090   -0.090
## 102   Im11 ~~ Im17   5.351 -0.061  -0.061   -0.177   -0.177
## 103 CHOICE =~  Im5   5.052  0.088   0.108    0.082    0.082
## 104 FRENCH =~ Im13   4.802 -0.157  -0.101   -0.084   -0.084
## 105   DECO =~ Im22   4.756  0.094   0.116    0.076    0.076
## 106   Im22 ~~ Im11   4.722  0.083   0.083    0.124    0.124
## 107 CHOICE =~ Im22   4.719  0.099   0.122    0.080    0.080
## 108   Im13 ~~ Im16   4.625 -0.073  -0.073   -0.118   -0.118
## 109   Im19 ~~ Im17   4.621  0.056   0.056    0.161    0.161
## 110  ATMOS =~ Im10   4.609 -0.038  -0.048   -0.055   -0.055
## 111  BRAND =~ Im10   4.570 -0.040  -0.048   -0.054   -0.054
## 112   Im14 ~~ Im22   4.494 -0.036  -0.036   -0.154   -0.154
## 113  ATMOS =~  Im4   4.422 -0.053  -0.067   -0.050   -0.050
## 114   Im14 ~~ Im15   4.415 -0.032  -0.032   -0.127   -0.127
## 115   Im21 ~~  Im9   4.370 -0.102  -0.102   -0.101   -0.101
## 116   Im10 ~~ Im13   4.362 -0.031  -0.031   -0.138   -0.138
## 117    Im7 ~~ Im15   4.358  0.074   0.074    0.098    0.098
## 118    Im3 ~~ Im22   4.300  0.047   0.047    0.135    0.135
## 119   Im20 ~~  Im1   4.283 -0.056  -0.056   -0.141   -0.141
## 120    Im4 ~~ Im16   4.262  0.048   0.048    0.149    0.149
## 121 FRENCH =~  Im5   4.167  0.144   0.093    0.070    0.070
## 122  ATMOS =~  Im8   4.061  0.057   0.072    0.068    0.068
## 123    Im6 ~~ Im20   4.039 -0.084  -0.084   -0.105   -0.105
## 124   Im10 ~~ Im11   4.002  0.036   0.036    0.111    0.111
## 125   Im20 ~~ Im17   3.990 -0.054  -0.054   -0.177   -0.177
## 126    Im6 ~~ Im11   3.977 -0.083  -0.083   -0.091   -0.091
## 127    Im5 ~~  Im1   3.869  0.051   0.051    0.117    0.117
## 128   Im15 ~~ Im17   3.695  0.045   0.045    0.147    0.147
## 129    Im4 ~~ Im18   3.604  0.035   0.035    0.152    0.152
## 130   Im12 ~~ Im15   3.556  0.050   0.050    0.110    0.110
## 131 FRENCH =~ Im17   3.536 -0.115  -0.074   -0.060   -0.060
## 132   Im14 ~~ Im16   3.474 -0.035  -0.035   -0.110   -0.110
## 133    Im3 ~~ Im15   3.381  0.037   0.037    0.099    0.099
## 134    Im3 ~~ Im17   3.375  0.029   0.029    0.161    0.161
## 135    Im3 ~~ Im19   3.371  0.040   0.040    0.096    0.096
## 136   Im13 ~~ Im15   3.338  0.051   0.051    0.102    0.102
## 137   Im22 ~~  Im1   3.275  0.049   0.049    0.132    0.132
## 138   Im20 ~~ Im13   3.270  0.057   0.057    0.115    0.115
## 139   Im13 ~~  Im2   3.219 -0.040  -0.040   -0.116   -0.116
## 140   Im11 ~~  Im1   3.071 -0.047  -0.047   -0.104   -0.104
## 141 CHOICE =~ Im21   3.048  0.074   0.091    0.066    0.066
## 142   Im10 ~~ Im17   3.000 -0.021  -0.021   -0.157   -0.157
## 143  ATMOS =~  Im1   2.962 -0.054  -0.068   -0.051   -0.051
## 144  ATMOS =~ Im13   2.889  0.062   0.078    0.065    0.065
## 145   Im16 ~~  Im9   2.810  0.089   0.089    0.076    0.076
## 146    Im5 ~~ Im14   2.794  0.028   0.028    0.101    0.101
## 147    Im4 ~~ Im22   2.701 -0.036  -0.036   -0.146   -0.146
## 148 CHOICE =~ Im10   2.670 -0.030  -0.037   -0.042   -0.042
## 149    Im1 ~~ Im17   2.662 -0.031  -0.031   -0.161   -0.161
## 150  ATMOS =~ Im14   2.649 -0.028  -0.035   -0.041   -0.041
## 151    Im4 ~~ Im19   2.526  0.034   0.034    0.113    0.113
## 152    Im4 ~~ Im11   2.492 -0.034  -0.034   -0.115   -0.115
## 153   Im21 ~~ Im18   2.456 -0.050  -0.050   -0.086   -0.086
## 154   Im12 ~~  Im2   2.343 -0.032  -0.032   -0.104   -0.104
## 155    Im6 ~~ Im15   2.316  0.057   0.057    0.070    0.070
## 156   Im12 ~~  Im9   2.302  0.057   0.057    0.086    0.086
## 157   DECO =~ Im12   2.287 -0.054  -0.067   -0.059   -0.059
## 158    Im6 ~~  Im1   2.248 -0.044  -0.044   -0.087   -0.087
## 159    Im3 ~~ Im20   2.237 -0.034  -0.034   -0.091   -0.091
## 160   Im15 ~~ Im18   2.236 -0.043  -0.043   -0.077   -0.077
## 161    Im7 ~~  Im1   2.236 -0.042  -0.042   -0.089   -0.089
## 162    Im6 ~~ Im12   2.164 -0.047  -0.047   -0.083   -0.083
## 163   Im10 ~~ Im12   2.160  0.020   0.020    0.102    0.102
## 164    Im4 ~~  Im2   2.090 -0.022  -0.022   -0.123   -0.123
## 165    Im5 ~~  Im6   1.873 -0.055  -0.055   -0.063   -0.063
## 166    Im4 ~~  Im6   1.846  0.032   0.032    0.096    0.096
## 167   DECO =~ Im10   1.832 -0.025  -0.031   -0.035   -0.035
## 168   Im22 ~~  Im2   1.825 -0.037  -0.037   -0.090   -0.090
## 169   Im10 ~~ Im22   1.781 -0.024  -0.024   -0.090   -0.090
## 170   Im12 ~~ Im17   1.776 -0.028  -0.028   -0.131   -0.131
## 171    Im6 ~~ Im18   1.754  0.047   0.047    0.066    0.066
## 172   Im21 ~~ Im17   1.749  0.035   0.035    0.108    0.108
## 173    Im5 ~~ Im16   1.746 -0.052  -0.052   -0.062   -0.062
## 174    Im3 ~~ Im12   1.732 -0.023  -0.023   -0.087   -0.087
## 175   Im22 ~~ Im13   1.726 -0.041  -0.041   -0.089   -0.089
## 176   Im18 ~~  Im9   1.696 -0.060  -0.060   -0.073   -0.073
## 177  ATMOS =~ Im17   1.682 -0.052  -0.065   -0.053   -0.053
## 178   QUAL =~  Im4   1.672 -0.060  -0.042   -0.031   -0.031
## 179   Im20 ~~ Im19   1.649  0.048   0.048    0.067    0.067
## 180   Im20 ~~  Im2   1.631 -0.035  -0.035   -0.080   -0.080
## 181 FRENCH =~ Im18   1.599 -0.082  -0.052   -0.038   -0.038
## 182    Im4 ~~ Im12   1.546  0.021   0.021    0.113    0.113
## 183 CHOICE =~ Im17   1.544  0.057   0.071    0.057    0.057
## 184    Im6 ~~ Im19   1.483  0.050   0.050    0.055    0.055
## 185   Im12 ~~ Im16   1.481  0.038   0.038    0.070    0.070
## 186    Im7 ~~ Im16   1.479 -0.052  -0.052   -0.056   -0.056
## 187   DECO =~ Im13   1.462  0.045   0.056    0.046    0.046
## 188 FRENCH =~ Im20   1.442 -0.089  -0.057   -0.038   -0.038
## 189   Im12 ~~ Im13   1.442  0.089   0.089    0.255    0.255
## 190  BRAND =~  Im3   1.434  0.033   0.039    0.030    0.030
## 191   Im12 ~~  Im1   1.360 -0.024  -0.024   -0.087   -0.087
## 192    Im3 ~~ Im18   1.301 -0.022  -0.022   -0.067   -0.067
## 193   Im16 ~~ Im17   1.269  0.032   0.032    0.085    0.085
## 194    Im3 ~~ Im11   1.261  0.025   0.025    0.060    0.060
## 195   Im14 ~~ Im17   1.252  0.013   0.013    0.110    0.110
## 196   Im10 ~~ Im19   1.233  0.019   0.019    0.060    0.060
## 197    Im3 ~~ Im10   1.230  0.012   0.012    0.070    0.070
## 198    Im8 ~~ Im18   1.200 -0.027  -0.027   -0.057   -0.057
## 199    Im8 ~~  Im1   1.194 -0.023  -0.023   -0.065   -0.065
## 200   Im21 ~~  Im2   1.185  0.030   0.030    0.063    0.063
## 201   QUAL =~ Im22   1.168 -0.084  -0.059   -0.038   -0.038
## 202 CHOICE =~ Im14   1.154  0.019   0.023    0.027    0.027
## 203   Im10 ~~  Im9   1.119  0.024   0.024    0.057    0.057
## 204   DECO =~ Im18   1.115  0.043   0.053    0.038    0.038
## 205 CHOICE =~  Im4   1.111 -0.028  -0.035   -0.026   -0.026
## 206   Im14 ~~ Im21   1.104  0.018   0.018    0.067    0.067
## 207    Im5 ~~ Im19   1.093 -0.038  -0.038   -0.048   -0.048
## 208    Im4 ~~  Im8   1.089  0.017   0.017    0.076    0.076
## 209   Im22 ~~ Im18   1.078  0.034   0.034    0.065    0.065
## 210   Im22 ~~ Im15   1.067  0.036   0.036    0.059    0.059
## 211   Im13 ~~ Im18   1.031 -0.027  -0.027   -0.062   -0.062
## 212 CHOICE =~  Im7   0.941  0.037   0.046    0.038    0.038
## 213    Im4 ~~ Im10   0.906 -0.010  -0.010   -0.082   -0.082
## 214    Im3 ~~ Im14   0.890 -0.010  -0.010   -0.065   -0.065
## 215   Im10 ~~  Im2   0.889 -0.012  -0.012   -0.061   -0.061
## 216  ATMOS =~  Im3   0.869  0.023   0.029    0.022    0.022
## 217   Im11 ~~ Im16   0.846  0.038   0.038    0.043    0.043
## 218   QUAL =~ Im14   0.840  0.031   0.022    0.026    0.026
## 219   QUAL =~ Im20   0.837  0.069   0.049    0.033    0.033
## 220    Im1 ~~ Im18   0.830  0.021   0.021    0.060    0.060
## 221    Im3 ~~ Im16   0.818  0.022   0.022    0.048    0.048
## 222   DECO =~  Im7   0.814  0.035   0.043    0.036    0.036
## 223    Im2 ~~ Im18   0.811 -0.021  -0.021   -0.054   -0.054
## 224   Im20 ~~ Im12   0.794  0.026   0.026    0.059    0.059
## 225 FRENCH =~ Im22   0.781  0.067   0.043    0.028    0.028
## 226   Im20 ~~ Im16   0.767  0.036   0.036    0.046    0.046
## 227   Im14 ~~ Im18   0.739 -0.012  -0.012   -0.056   -0.056
## 228   Im22 ~~ Im19   0.717 -0.032  -0.032   -0.047   -0.047
## 229   QUAL =~ Im10   0.654 -0.028  -0.020   -0.023   -0.023
## 230   Im14 ~~ Im13   0.649  0.011   0.011    0.057    0.057
## 231   Im14 ~~ Im11   0.639  0.014   0.014    0.048    0.048
## 232 CHOICE =~  Im6   0.612  0.032   0.039    0.033    0.033
## 233   Im19 ~~  Im9   0.595  0.037   0.037    0.035    0.035
## 234  BRAND =~ Im11   0.591 -0.036  -0.043   -0.038   -0.038
## 235    Im6 ~~  Im2   0.577 -0.023  -0.023   -0.040   -0.040
## 236   Im20 ~~ Im15   0.576  0.026   0.026    0.041    0.041
## 237    Im5 ~~ Im22   0.561  0.027   0.027    0.043    0.043
## 238    Im8 ~~ Im19   0.558  0.022   0.022    0.035    0.035
## 239    Im8 ~~ Im21   0.538 -0.022  -0.022   -0.037   -0.037
## 240   Im21 ~~ Im12   0.537  0.021   0.021    0.045    0.045
## 241   Im11 ~~ Im19   0.536  0.028   0.028    0.034    0.034
## 242   Im21 ~~  Im1   0.534  0.020   0.020    0.046    0.046
## 243   QUAL =~  Im7   0.517  0.053   0.037    0.031    0.031
## 244   Im10 ~~ Im18   0.516  0.011   0.011    0.044    0.044
## 245    Im5 ~~ Im11   0.511  0.026   0.026    0.034    0.034
## 246   Im10 ~~ Im20   0.483  0.012   0.012    0.044    0.044
## 247   Im12 ~~ Im18   0.465 -0.017  -0.017   -0.044   -0.044
## 248   Im14 ~~  Im1   0.460  0.008   0.008    0.052    0.052
## 249 FRENCH =~  Im3   0.457 -0.031  -0.020   -0.015   -0.015
## 250   Im20 ~~ Im11   0.453  0.026   0.026    0.036    0.036
## 251    Im3 ~~  Im8   0.442 -0.012  -0.012   -0.036   -0.036
## 252   Im20 ~~ Im18   0.417  0.021   0.021    0.038    0.038
## 253   Im20 ~~ Im22   0.407  0.061   0.061    0.103    0.103
## 254   Im10 ~~  Im1   0.405 -0.008  -0.008   -0.045   -0.045
## 255    Im5 ~~ Im20   0.402  0.023   0.023    0.034    0.034
## 256  BRAND =~ Im14   0.390 -0.011  -0.014   -0.016   -0.016
## 257    Im2 ~~  Im9   0.381 -0.022  -0.022   -0.033   -0.033
## 258   Im21 ~~ Im11   0.373 -0.023  -0.023   -0.030   -0.030
## 259   Im16 ~~ Im18   0.357 -0.021  -0.021   -0.030   -0.030
## 260    Im5 ~~ Im15   0.339 -0.019  -0.019   -0.028   -0.028
## 261   Im21 ~~ Im13   0.328 -0.018  -0.018   -0.034   -0.034
## 262   QUAL =~  Im8   0.320 -0.031  -0.022   -0.021   -0.021
## 263    Im5 ~~ Im21   0.319 -0.021  -0.021   -0.028   -0.028
## 264   DECO =~  Im8   0.317  0.016   0.020    0.019    0.019
## 265    Im7 ~~ Im19   0.317  0.022   0.022    0.026    0.026
## 266    Im4 ~~ Im20   0.315  0.012   0.012    0.047    0.047
## 267   Im11 ~~  Im2   0.310  0.015   0.015    0.030    0.030
## 268    Im5 ~~  Im8   0.298 -0.015  -0.015   -0.026   -0.026
## 269    Im7 ~~ Im20   0.292 -0.021  -0.021   -0.029   -0.029
## 270    Im4 ~~ Im13   0.275 -0.009  -0.009   -0.045   -0.045
## 271    Im3 ~~ Im13   0.274  0.010   0.010    0.033    0.033
## 272    Im8 ~~ Im13   0.252 -0.012  -0.012   -0.028   -0.028
## 273   DECO =~ Im11   0.240  0.019   0.024    0.021    0.021
## 274   Im12 ~~ Im19   0.218  0.013   0.013    0.027    0.027
## 275    Im4 ~~  Im5   0.193  0.017   0.017    0.059    0.059
## 276    Im3 ~~  Im7   0.193 -0.010  -0.010   -0.024   -0.024
## 277    Im7 ~~ Im12   0.191 -0.013  -0.013   -0.025   -0.025
## 278    Im5 ~~ Im17   0.190  0.011   0.011    0.033    0.033
## 279    Im7 ~~ Im21   0.188 -0.017  -0.017   -0.022   -0.022
## 280    Im5 ~~  Im9   0.179  0.020   0.020    0.019    0.019
## 281   Im19 ~~ Im18   0.174 -0.013  -0.013   -0.021   -0.021
## 282   Im21 ~~ Im16   0.170 -0.017  -0.017   -0.020   -0.020
## 283 FRENCH =~  Im4   0.152 -0.018  -0.012   -0.009   -0.009
## 284    Im4 ~~ Im15   0.151 -0.008  -0.008   -0.028   -0.028
## 285   Im21 ~~ Im19   0.149 -0.014  -0.014   -0.019   -0.019
## 286   DECO =~ Im14   0.132 -0.007  -0.008   -0.009   -0.009
## 287    Im4 ~~  Im1   0.125  0.005   0.005    0.033    0.033
## 288    Im3 ~~  Im2   0.124  0.006   0.006    0.022    0.022
## 289    Im2 ~~ Im17   0.116  0.006   0.006    0.031    0.031
## 290   Im10 ~~ Im15   0.108 -0.005  -0.005   -0.018   -0.018
## 291    Im5 ~~ Im10   0.106 -0.006  -0.006   -0.018   -0.018
## 292 FRENCH =~ Im21   0.106  0.023   0.015    0.011    0.011
## 293    Im6 ~~ Im16   0.097 -0.014  -0.014   -0.014   -0.014
## 294 CHOICE =~  Im8   0.094 -0.009  -0.011   -0.010   -0.010
## 295    Im7 ~~ Im11   0.091 -0.012  -0.012   -0.014   -0.014
## 296   Im10 ~~ Im21   0.089 -0.005  -0.005   -0.018   -0.018
## 297   Im11 ~~ Im18   0.089  0.010   0.010    0.015    0.015
## 298    Im5 ~~  Im2   0.087 -0.008  -0.008   -0.016   -0.016
## 299    Im7 ~~ Im18   0.086 -0.010  -0.010   -0.015   -0.015
## 300   QUAL =~  Im6   0.086 -0.023  -0.016   -0.013   -0.013
## 301    Im5 ~~ Im12   0.084  0.008   0.008    0.017    0.017
## 302 CHOICE =~ Im11   0.082 -0.012  -0.015   -0.013   -0.013
## 303    Im8 ~~ Im12   0.076 -0.006  -0.006   -0.016   -0.016
## 304    Im6 ~~ Im13   0.071  0.009   0.009    0.014    0.014
## 305   Im14 ~~ Im20   0.068 -0.004  -0.004   -0.018   -0.018
## 306    Im5 ~~  Im7   0.064  0.010   0.010    0.012    0.012
## 307   Im22 ~~ Im17   0.054  0.006   0.006    0.022    0.022
## 308    Im6 ~~ Im21   0.052 -0.010  -0.010   -0.011   -0.011
## 309   QUAL =~ Im21   0.051  0.016   0.011    0.008    0.008
## 310    Im4 ~~ Im21   0.046  0.005   0.005    0.017    0.017
## 311   Im21 ~~ Im15   0.040 -0.007  -0.007   -0.010   -0.010
## 312   Im14 ~~ Im12   0.039 -0.003  -0.003   -0.015   -0.015
## 313    Im7 ~~ Im13   0.037 -0.006  -0.006   -0.011   -0.011
## 314    Im8 ~~ Im17   0.036 -0.004  -0.004   -0.015   -0.015
## 315   QUAL =~ Im17   0.035 -0.015  -0.011   -0.009   -0.009
## 316  BRAND =~ Im21   0.027 -0.007  -0.009   -0.006   -0.006
## 317   Im14 ~~ Im19   0.027  0.003   0.003    0.010    0.010
## 318   Im20 ~~  Im9   0.021  0.007   0.007    0.008    0.008
## 319    Im7 ~~ Im17   0.021 -0.004  -0.004   -0.011   -0.011
## 320  BRAND =~  Im8   0.020  0.004   0.005    0.005    0.005
## 321 CHOICE =~  Im3   0.018 -0.004  -0.004   -0.003   -0.003
## 322    Im3 ~~  Im9   0.018 -0.004  -0.004   -0.007   -0.007
## 323    Im5 ~~ Im18   0.017  0.004   0.004    0.007    0.007
## 324   DECO =~ Im21   0.017  0.005   0.006    0.005    0.005
## 325    Im8 ~~ Im20   0.014  0.003   0.003    0.006    0.006
## 326    Im4 ~~  Im9   0.014 -0.003  -0.003   -0.008   -0.008
## 327    Im3 ~~ Im21   0.010 -0.002  -0.002   -0.006   -0.006
## 328  ATMOS =~ Im18   0.009  0.004   0.005    0.004    0.004
## 329   Im11 ~~ Im15   0.007 -0.003  -0.003   -0.004   -0.004
## 330    Im7 ~~  Im2   0.006 -0.002  -0.002   -0.004   -0.004
## 331 FRENCH =~ Im12   0.002 -0.003  -0.002   -0.002   -0.002
## 332   Im13 ~~  Im9   0.002  0.002   0.002    0.003    0.003
## 333    Im4 ~~ Im14   0.002  0.000   0.000   -0.004   -0.004
## 334    Im4 ~~  Im7   0.002 -0.001  -0.001   -0.003   -0.003
## 335    Im8 ~~ Im11   0.002  0.001   0.001    0.002    0.002
## 336   Im13 ~~ Im19   0.002  0.001   0.001    0.002    0.002
## 337    Im3 ~~  Im6   0.002  0.001   0.001    0.002    0.002
## 338   Im22 ~~ Im16   0.001  0.001   0.001    0.002    0.002
## 339   QUAL =~  Im3   0.001  0.001   0.001    0.001    0.001
## 340    Im6 ~~ Im17   0.000  0.000   0.000   -0.001   -0.001
## 341    Im5 ~~ Im13   0.000  0.000   0.000    0.000    0.000

2.3.2 7 factor model

Based on the modification indices we create a new model

# # no excluded variables:
# CFA_model_img_7f <- "
# DECO =~ Im3 + Im4 + Im5
# FOOD =~ Im8 + Im10 + Im14
# ATMOS =~ Im20 + Im21 + Im22
# PRODQUAL =~ Im11 + Im12 + Im13
# CHOICE =~ Im1 + Im2 + Im15 + Im16 + Im19
# BRAND =~ Im17 + Im18
# FRENCH =~ Im6 + Im7 + Im9
# "

# MIs indicate separate Im1, Im2 and Im16, Im19 no excluded variables
# Im8 under FRENCH
# exclude Im8 
# exclude Im15
# exclude Im9
CFA_model_img_7f <- "
DECO =~ Im3 + Im4 + Im5
FOOD =~ Im10 + Im14
ATMOS =~ Im20 + Im21 + Im22
PRODQUAL =~ Im11 + Im12 + Im13
CHOICE =~ Im1 + Im2  
PROF =~ Im16 + Im19
BRAND =~ Im17 + Im18
FRENCH =~ Im6 + Im7
"

# # excluded variables: Im9, Im15, Im16, Im19
# CFA_model_img_7f <- "
# QUAL =~ Im11 + Im12 + Im13
# FOOD =~ Im8 + Im10 + Im14
# ATMOS =~ Im20 + Im21 + Im22
# DECO =~ Im3 + Im4 + Im5
# CHOICE =~ Im1 + Im2
# BRAND =~ Im17 + Im18
# FRENCH =~ Im6 + Im7
# "

# # excluded variables: Im9, Im15, Im16, Im19, Im8
# CFA_model_img_7f <- "
# QUAL =~ Im11 + Im12 + Im13
# FOOD =~ Im10 + Im14
# ATMOS =~ Im20 + Im21 + Im22
# DECO =~ Im3 + Im4 + Im5
# CHOICE =~ Im1 + Im2
# BRAND =~ Im17 + Im18
# FRENCH =~ Im6 + Im7
# "

# # 8 factor model: excluded variables: Im9, Im15, Im8, Im11
# CFA_model_img_7f <- "
# QUAL =~ Im12 + Im13
# FOOD =~ Im10 + Im14
# ATMOS =~ Im20 + Im21 + Im22
# DECO =~ Im3 + Im4 + Im5
# CHOICE =~ Im1 + Im2
# BRAND =~ Im17 + Im18
# FRENCH =~ Im6 + Im7
# PROF =~ Im16 + Im19
# "


CFA_fit_img_7f <- cfa(CFA_model_img_7f, data=survey, missing="ML")
summary(CFA_fit_img_7f, fit.measures=TRUE, standardized=TRUE)

## lavaan 0.6.15 ended normally after 108 iterations
## 
##   Estimator                                         ML
##   Optimization method                           NLMINB
##   Number of model parameters                        85
## 
##   Number of observations                           553
##   Number of missing patterns                        79
## 
## Model Test User Model:
##                                                       
##   Test statistic                               259.047
##   Degrees of freedom                               124
##   P-value (Chi-square)                           0.000
## 
## Model Test Baseline Model:
## 
##   Test statistic                              7474.765
##   Degrees of freedom                               171
##   P-value                                        0.000
## 
## User Model versus Baseline Model:
## 
##   Comparative Fit Index (CFI)                    0.982
##   Tucker-Lewis Index (TLI)                       0.975
##                                                       
##   Robust Comparative Fit Index (CFI)             0.981
##   Robust Tucker-Lewis Index (TLI)                0.974
## 
## Loglikelihood and Information Criteria:
## 
##   Loglikelihood user model (H0)             -12973.111
##   Loglikelihood unrestricted model (H1)     -12843.588
##                                                       
##   Akaike (AIC)                               26116.223
##   Bayesian (BIC)                             26483.028
##   Sample-size adjusted Bayesian (SABIC)      26213.200
## 
## Root Mean Square Error of Approximation:
## 
##   RMSEA                                          0.044
##   90 Percent confidence interval - lower         0.037
##   90 Percent confidence interval - upper         0.052
##   P-value H_0: RMSEA <= 0.050                    0.886
##   P-value H_0: RMSEA >= 0.080                    0.000
##                                                       
##   Robust RMSEA                                   0.045
##   90 Percent confidence interval - lower         0.038
##   90 Percent confidence interval - upper         0.053
##   P-value H_0: Robust RMSEA <= 0.050             0.825
##   P-value H_0: Robust RMSEA >= 0.080             0.000
## 
## Standardized Root Mean Square Residual:
## 
##   SRMR                                           0.029
## 
## Parameter Estimates:
## 
##   Standard errors                             Standard
##   Information                                 Observed
##   Observed information based on                Hessian
## 
## Latent Variables:
##                    Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
##   DECO =~                                                               
##     Im3               1.000                               1.236    0.937
##     Im4               1.056    0.025   42.717    0.000    1.305    0.969
##     Im5               0.818    0.034   23.815    0.000    1.011    0.760
##   FOOD =~                                                               
##     Im10              1.000                               0.812    0.923
##     Im14              1.015    0.036   28.479    0.000    0.824    0.952
##   ATMOS =~                                                              
##     Im20              1.000                               1.265    0.845
##     Im21              0.849    0.041   20.823    0.000    1.074    0.783
##     Im22              1.060    0.047   22.606    0.000    1.340    0.877
##   PRODQUAL =~                                                           
##     Im11              1.000                               0.703    0.615
##     Im12              1.410    0.094   15.046    0.000    0.991    0.872
##     Im13              1.465    0.105   13.968    0.000    1.030    0.855
##   CHOICE =~                                                             
##     Im1               1.000                               1.305    0.980
##     Im2               0.885    0.033   27.043    0.000    1.155    0.899
##   PROF =~                                                               
##     Im16              1.000                               0.921    0.766
##     Im19              1.046    0.061   17.170    0.000    0.963    0.856
##   BRAND =~                                                              
##     Im17              1.000                               1.204    0.969
##     Im18              0.994    0.041   24.143    0.000    1.197    0.856
##   FRENCH =~                                                             
##     Im6               1.000                               0.975    0.813
##     Im7               1.184    0.071   16.770    0.000    1.155    0.955
## 
## Covariances:
##                    Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
##   DECO ~~                                                               
##     FOOD              0.418    0.050    8.393    0.000    0.416    0.416
##     ATMOS             0.730    0.082    8.912    0.000    0.467    0.467
##     PRODQUAL          0.409    0.051    8.040    0.000    0.471    0.471
##     CHOICE            0.711    0.079    9.032    0.000    0.441    0.441
##     PROF              0.743    0.071   10.465    0.000    0.653    0.653
##     BRAND             0.770    0.076   10.140    0.000    0.517    0.517
##     FRENCH            0.402    0.063    6.350    0.000    0.334    0.334
##   FOOD ~~                                                               
##     ATMOS             0.303    0.051    5.948    0.000    0.295    0.295
##     PRODQUAL          0.258    0.034    7.662    0.000    0.452    0.452
##     CHOICE            0.328    0.050    6.584    0.000    0.309    0.309
##     PROF              0.372    0.043    8.589    0.000    0.498    0.498
##     BRAND             0.318    0.047    6.801    0.000    0.325    0.325
##     FRENCH            0.463    0.047    9.829    0.000    0.585    0.585
##   ATMOS ~~                                                              
##     PRODQUAL          0.372    0.053    7.011    0.000    0.418    0.418
##     CHOICE            0.739    0.085    8.728    0.000    0.448    0.448
##     PROF              0.557    0.069    8.089    0.000    0.478    0.478
##     BRAND             0.787    0.081    9.715    0.000    0.516    0.516
##     FRENCH            0.410    0.065    6.352    0.000    0.333    0.333
##   PRODQUAL ~~                                                           
##     CHOICE            0.439    0.054    8.161    0.000    0.478    0.478
##     PROF              0.343    0.043    7.946    0.000    0.529    0.529
##     BRAND             0.479    0.053    9.046    0.000    0.566    0.566
##     FRENCH            0.210    0.037    5.622    0.000    0.306    0.306
##   CHOICE ~~                                                             
##     PROF              0.717    0.072    9.956    0.000    0.597    0.597
##     BRAND             0.817    0.079   10.362    0.000    0.519    0.519
##     FRENCH            0.286    0.060    4.735    0.000    0.225    0.225
##   PROF ~~                                                               
##     BRAND             0.667    0.066   10.040    0.000    0.601    0.601
##     FRENCH            0.328    0.051    6.438    0.000    0.366    0.366
##   BRAND ~~                                                              
##     FRENCH            0.378    0.061    6.175    0.000    0.322    0.322
## 
## Intercepts:
##                    Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
##    .Im3               4.995    0.056   88.560    0.000    4.995    3.786
##    .Im4               4.999    0.057   86.983    0.000    4.999    3.712
##    .Im5               5.035    0.057   87.844    0.000    5.035    3.787
##    .Im10              6.100    0.037  162.789    0.000    6.100    6.937
##    .Im14              6.138    0.037  165.861    0.000    6.138    7.093
##    .Im20              4.672    0.064   73.177    0.000    4.672    3.123
##    .Im21              5.139    0.058   87.970    0.000    5.139    3.751
##    .Im22              4.279    0.065   65.401    0.000    4.279    2.799
##    .Im11              5.653    0.049  115.271    0.000    5.653    4.943
##    .Im12              5.666    0.049  116.089    0.000    5.666    4.983
##    .Im13              5.448    0.052  105.615    0.000    5.448    4.524
##    .Im1               4.790    0.057   84.202    0.000    4.790    3.597
##    .Im2               4.857    0.055   88.354    0.000    4.857    3.779
##    .Im16              5.135    0.052   99.147    0.000    5.135    4.269
##    .Im19              5.145    0.048  106.948    0.000    5.145    4.574
##    .Im17              5.025    0.053   94.519    0.000    5.025    4.041
##    .Im18              4.595    0.060   76.447    0.000    4.595    3.287
##    .Im6               5.827    0.051  113.784    0.000    5.827    4.858
##    .Im7               5.753    0.052  110.826    0.000    5.753    4.756
##     DECO              0.000                               0.000    0.000
##     FOOD              0.000                               0.000    0.000
##     ATMOS             0.000                               0.000    0.000
##     PRODQUAL          0.000                               0.000    0.000
##     CHOICE            0.000                               0.000    0.000
##     PROF              0.000                               0.000    0.000
##     BRAND             0.000                               0.000    0.000
##     FRENCH            0.000                               0.000    0.000
## 
## Variances:
##                    Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
##    .Im3               0.213    0.024    8.755    0.000    0.213    0.122
##    .Im4               0.109    0.024    4.532    0.000    0.109    0.060
##    .Im5               0.747    0.049   15.217    0.000    0.747    0.422
##    .Im10              0.114    0.019    5.961    0.000    0.114    0.148
##    .Im14              0.070    0.019    3.680    0.000    0.070    0.093
##    .Im20              0.638    0.061   10.451    0.000    0.638    0.285
##    .Im21              0.725    0.057   12.672    0.000    0.725    0.386
##    .Im22              0.541    0.063    8.539    0.000    0.541    0.231
##    .Im11              0.814    0.055   14.802    0.000    0.814    0.622
##    .Im12              0.310    0.040    7.845    0.000    0.310    0.240
##    .Im13              0.390    0.045    8.765    0.000    0.390    0.269
##    .Im1               0.070    0.050    1.394    0.163    0.070    0.040
##    .Im2               0.317    0.044    7.233    0.000    0.317    0.192
##    .Im16              0.599    0.052   11.498    0.000    0.599    0.414
##    .Im19              0.338    0.045    7.457    0.000    0.338    0.267
##    .Im17              0.095    0.045    2.112    0.035    0.095    0.062
##    .Im18              0.521    0.055    9.540    0.000    0.521    0.267
##    .Im6               0.487    0.056    8.677    0.000    0.487    0.339
##    .Im7               0.128    0.067    1.930    0.054    0.128    0.088
##     DECO              1.528    0.107   14.326    0.000    1.000    1.000
##     FOOD              0.659    0.049   13.328    0.000    1.000    1.000
##     ATMOS             1.599    0.138   11.623    0.000    1.000    1.000
##     PRODQUAL          0.494    0.067    7.361    0.000    1.000    1.000
##     CHOICE            1.704    0.118   14.388    0.000    1.000    1.000
##     PROF              0.849    0.088    9.638    0.000    1.000    1.000
##     BRAND             1.451    0.104   13.988    0.000    1.000    1.000
##     FRENCH            0.952    0.095   10.058    0.000    1.000    1.000

2.3.2.1 Discussion of global fit measures

Chi square: p-value > 0.05

RMSEA RMSEA <= 0.05 Good fit 0.05 < RMSEA <= 0.08 Acceptable fit 0.08 < RMSEA <= 0.10 Bad fit RMSEA > 0.1 Unacceptable fit

CFI CFI < 0.90 definitely reject model 0.90 < CFI < 0.95 high underrejection rates for misspecified models CFI > 0.95 accept model

2.3.2.2 local fit measures

# semPaths(CFA_fit_img_7f, what = "path", whatLabels = "std", style = "mx",
#          rotation = 2, layout = "tree3", mar = c(1, 2, 1, 2), 
#          nCharNodes = 7,shapeMan = "rectangle", sizeMan = 8, sizeMan2 = 5, 
#          curvePivot=TRUE, edge.label.cex = 1.2, edge.color = "skyblue4")


semPaths(CFA_fit_img_7f, what = "path", whatLabels = "std", style = "mx",
         rotation = 2, layout = "tree3", mar = c(1, 2, 1, 2), 
         nCharNodes = 7,shapeMan = "rectangle", 
         sizeMan = 4, sizeMan2 = 3, sizeInt = 2, sizeLat = 6, asize = 1.5,
         curvePivot=TRUE, edge.label.cex = .8, edge.color = "skyblue4"
         )

lambda = inspect(CFA_fit_img_7f, what="std")$lambda
theta = inspect(CFA_fit_img_7f, what="std")$theta

# create lambda matrix with ones instead of std.all
ones <- lambda
ones[ones>0] <- 1

# a matrix with dimensions of lambda matrix but with lambdas replaced by thetas
theta_lb <- theta %*% ones

2.3.2.2.1 Indicator reliability criterion (Individual Item Reliability)

# JONATHAN
# calculate indicator reliabilities (should be larger than 0.4)
indicrel <- lambda^2/(lambda^2 + theta_lb)
# indicrel

# replace all values satisfying condition with NaN for visibility
indicrel_fail <- indicrel
indicrel_fail[indicrel_fail>.4] <- NaN
indicrel_fail

##      DECO FOOD ATMOS PRODQU CHOICE PROF BRAND FRENCH
## Im3   NaN  NaN   NaN    NaN    NaN  NaN   NaN    NaN
## Im4   NaN  NaN   NaN    NaN    NaN  NaN   NaN    NaN
## Im5   NaN  NaN   NaN    NaN    NaN  NaN   NaN    NaN
## Im10  NaN  NaN   NaN    NaN    NaN  NaN   NaN    NaN
## Im14  NaN  NaN   NaN    NaN    NaN  NaN   NaN    NaN
## Im20  NaN  NaN   NaN    NaN    NaN  NaN   NaN    NaN
## Im21  NaN  NaN   NaN    NaN    NaN  NaN   NaN    NaN
## Im22  NaN  NaN   NaN    NaN    NaN  NaN   NaN    NaN
## Im11  NaN  NaN   NaN  0.378    NaN  NaN   NaN    NaN
## Im12  NaN  NaN   NaN    NaN    NaN  NaN   NaN    NaN
## Im13  NaN  NaN   NaN    NaN    NaN  NaN   NaN    NaN
## Im1   NaN  NaN   NaN    NaN    NaN  NaN   NaN    NaN
## Im2   NaN  NaN   NaN    NaN    NaN  NaN   NaN    NaN
## Im16  NaN  NaN   NaN    NaN    NaN  NaN   NaN    NaN
## Im19  NaN  NaN   NaN    NaN    NaN  NaN   NaN    NaN
## Im17  NaN  NaN   NaN    NaN    NaN  NaN   NaN    NaN
## Im18  NaN  NaN   NaN    NaN    NaN  NaN   NaN    NaN
## Im6   NaN  NaN   NaN    NaN    NaN  NaN   NaN    NaN
## Im7   NaN  NaN   NaN    NaN    NaN  NaN   NaN    NaN

# FERESHTEH
#Local Fit

std.loadings<- inspect(CFA_fit_img_7f, what="std")$lambda
check=std.loadings
check[check>0] <- 1
std.loadings[std.loadings==0] <- NA
std.loadings2 <- std.loadings^2
std.theta<- inspect(CFA_fit_img_7f, what="std")$theta

#Individual item Reliability
IIR=std.loadings2/(colSums(std.theta)+std.loadings2)
IIR

##       DECO  FOOD ATMOS PRODQU CHOICE  PROF BRAND FRENCH
## Im3  0.878    NA    NA     NA     NA    NA    NA     NA
## Im4  0.940    NA    NA     NA     NA    NA    NA     NA
## Im5  0.578    NA    NA     NA     NA    NA    NA     NA
## Im10    NA 0.852    NA     NA     NA    NA    NA     NA
## Im14    NA 0.907    NA     NA     NA    NA    NA     NA
## Im20    NA    NA 0.715     NA     NA    NA    NA     NA
## Im21    NA    NA 0.614     NA     NA    NA    NA     NA
## Im22    NA    NA 0.769     NA     NA    NA    NA     NA
## Im11    NA    NA    NA  0.378     NA    NA    NA     NA
## Im12    NA    NA    NA  0.760     NA    NA    NA     NA
## Im13    NA    NA    NA  0.731     NA    NA    NA     NA
## Im1     NA    NA    NA     NA  0.960    NA    NA     NA
## Im2     NA    NA    NA     NA  0.808    NA    NA     NA
## Im16    NA    NA    NA     NA     NA 0.586    NA     NA
## Im19    NA    NA    NA     NA     NA 0.733    NA     NA
## Im17    NA    NA    NA     NA     NA    NA 0.938     NA
## Im18    NA    NA    NA     NA     NA    NA 0.733     NA
## Im6     NA    NA    NA     NA     NA    NA    NA  0.661
## Im7     NA    NA    NA     NA     NA    NA    NA  0.912

2.3.2.2.2 Construct reliability criterion

# JONATHAN
# calculate construct reliability (should be above .6)
constrrel <- (t(lambda) %*% ones)^2 / ((t(lambda) %*% ones)^2 + t(theta_lb) %*% ones )
# constrrel

# replace all values satisfying condition with NaN for visibility
constrrel_fail <- constrrel
constrrel_fail[constrrel_fail>.6] <- NaN
constrrel_fail

##          DECO FOOD ATMOS PRODQUAL CHOICE PROF BRAND FRENCH
## DECO      NaN  NaN   NaN      NaN    NaN  NaN   NaN    NaN
## FOOD      NaN  NaN   NaN      NaN    NaN  NaN   NaN    NaN
## ATMOS     NaN  NaN   NaN      NaN    NaN  NaN   NaN    NaN
## PRODQUAL  NaN  NaN   NaN      NaN    NaN  NaN   NaN    NaN
## CHOICE    NaN  NaN   NaN      NaN    NaN  NaN   NaN    NaN
## PROF      NaN  NaN   NaN      NaN    NaN  NaN   NaN    NaN
## BRAND     NaN  NaN   NaN      NaN    NaN  NaN   NaN    NaN
## FRENCH    NaN  NaN   NaN      NaN    NaN  NaN   NaN    NaN

# FERESHTEH
#Composite/Construct Reliability
sum.std.loadings<-colSums(std.loadings, na.rm=TRUE)^2
sum.std.theta<-rowSums(std.theta)
sum.std.theta=check*sum.std.theta
CR=sum.std.loadings/(sum.std.loadings+colSums(sum.std.theta))
CR

##      DECO      FOOD     ATMOS  PRODQUAL    CHOICE      PROF     BRAND    FRENCH 
## 0.9215974 0.9359401 0.8742538 0.8289772 0.9384579 0.7945651 0.9102910 0.8799457

2.3.2.2.3 Average Variance Extracted criterion

# JONATHAN
# calculate Average Variance Extracted (should be above .5)
AVE <- (t(lambda) %*% lambda) / (t(lambda) %*% lambda + t(theta_lb) %*% ones )
# avgvar

# replace all values satisfying condition with NaN for visibility
AVE_fail <- AVE
AVE_fail[AVE_fail>.5] <- NaN
AVE_fail

##          DECO FOOD ATMOS PRODQUAL CHOICE PROF BRAND FRENCH
## DECO      NaN  NaN   NaN      NaN    NaN  NaN   NaN    NaN
## FOOD      NaN  NaN   NaN      NaN    NaN  NaN   NaN    NaN
## ATMOS     NaN  NaN   NaN      NaN    NaN  NaN   NaN    NaN
## PRODQUAL  NaN  NaN   NaN      NaN    NaN  NaN   NaN    NaN
## CHOICE    NaN  NaN   NaN      NaN    NaN  NaN   NaN    NaN
## PROF      NaN  NaN   NaN      NaN    NaN  NaN   NaN    NaN
## BRAND     NaN  NaN   NaN      NaN    NaN  NaN   NaN    NaN
## FRENCH    NaN  NaN   NaN      NaN    NaN  NaN   NaN    NaN

# FERESHTEH
#Average Variance Extracted 
std.loadings<- inspect(CFA_fit_img_7f, what="std")$lambda
std.loadings <- std.loadings^2
AVE_fshteh=colSums(std.loadings)/(colSums(sum.std.theta)+colSums(std.loadings))
AVE_fshteh

##      DECO      FOOD     ATMOS  PRODQUAL    CHOICE      PROF     BRAND    FRENCH 
## 0.7983933 0.8796192 0.6990218 0.6229770 0.8842421 0.6598497 0.8358722 0.7867070

2.3.2.2.4 Fornell-Larcker Criteria

# JONATHAN
# correlations between constructs (factors...) should be lower than .7
psi = inspect(CFA_fit_img_7f, what="std")$psi
psi_fail <- psi
psi_fail[psi_fail<.7] <- NaN
psi_fail

##          DECO FOOD ATMOS PRODQU CHOICE PROF BRAND FRENCH
## DECO        1                                           
## FOOD      NaN    1                                      
## ATMOS     NaN  NaN     1                                
## PRODQUAL  NaN  NaN   NaN      1                         
## CHOICE    NaN  NaN   NaN    NaN      1                  
## PROF      NaN  NaN   NaN    NaN    NaN    1             
## BRAND     NaN  NaN   NaN    NaN    NaN  NaN     1       
## FRENCH    NaN  NaN   NaN    NaN    NaN  NaN   NaN      1

# JONATHAN
# AVE should be higher than squared correlations between constructs

#psi matrix squared
psi2 <- psi^2

# replace diagonal of psi matrix with AVE values
psi2 <- psi2 - psi2 * diag(1,nrow(psi2),ncol(psi2)) + diag(AVE) * diag(1,nrow(AVE),ncol(AVE))

# create matrix with columns filled with AVE
AVE_full <- AVE
AVE_full[is.na(AVE_full)] <- 0 #replace NAs with 0s
AVE_full <- AVE_full^0 %*% AVE_full # multiply a matrix full of ones with AVE_full to get columns filled with AVE

# substract matrices any psi bigger than AVE will be negative
AVEpsi_fail <- AVE_full - psi2
# AVE_full - psi2
AVEpsi_fail[AVEpsi_fail >= 0] <- NaN

AVE_full

##               DECO      FOOD     ATMOS PRODQUAL    CHOICE      PROF     BRAND
## DECO     0.7983933 0.8796192 0.6990218 0.622977 0.8842421 0.6598497 0.8358722
## FOOD     0.7983933 0.8796192 0.6990218 0.622977 0.8842421 0.6598497 0.8358722
## ATMOS    0.7983933 0.8796192 0.6990218 0.622977 0.8842421 0.6598497 0.8358722
## PRODQUAL 0.7983933 0.8796192 0.6990218 0.622977 0.8842421 0.6598497 0.8358722
## CHOICE   0.7983933 0.8796192 0.6990218 0.622977 0.8842421 0.6598497 0.8358722
## PROF     0.7983933 0.8796192 0.6990218 0.622977 0.8842421 0.6598497 0.8358722
## BRAND    0.7983933 0.8796192 0.6990218 0.622977 0.8842421 0.6598497 0.8358722
## FRENCH   0.7983933 0.8796192 0.6990218 0.622977 0.8842421 0.6598497 0.8358722
##            FRENCH
## DECO     0.786707
## FOOD     0.786707
## ATMOS    0.786707
## PRODQUAL 0.786707
## CHOICE   0.786707
## PROF     0.786707
## BRAND    0.786707
## FRENCH   0.786707

psi2

##           DECO  FOOD ATMOS PRODQU CHOICE  PROF BRAND FRENCH
## DECO     0.798                                             
## FOOD     0.173 0.880                                       
## ATMOS    0.218 0.087 0.699                                 
## PRODQUAL 0.222 0.205 0.175  0.623                          
## CHOICE   0.194 0.096 0.201  0.228  0.884                   
## PROF     0.426 0.248 0.228  0.280  0.356 0.660             
## BRAND    0.268 0.106 0.267  0.321  0.270 0.361 0.836       
## FRENCH   0.111 0.343 0.111  0.093  0.051 0.134 0.104  0.787

AVEpsi_fail

##            DECO   FOOD  ATMOS PRODQU CHOICE   PROF  BRAND FRENCH
## DECO          .                                                 
## FOOD        NaN      .                                          
## ATMOS       NaN    NaN      .                                   
## PRODQUAL    NaN    NaN    NaN      .                            
## CHOICE      NaN    NaN    NaN    NaN      .                     
## PROF        NaN    NaN    NaN    NaN    NaN      .              
## BRAND       NaN    NaN    NaN    NaN    NaN    NaN      .       
## FRENCH      NaN    NaN    NaN    NaN    NaN    NaN    NaN      .

# FERESHTEH
std_fit1=inspect(CFA_fit_img_7f, "std")
std_fit1$psi^2

##           DECO  FOOD ATMOS PRODQU CHOICE  PROF BRAND FRENCH
## DECO     1.000                                             
## FOOD     0.173 1.000                                       
## ATMOS    0.218 0.087 1.000                                 
## PRODQUAL 0.222 0.205 0.175  1.000                          
## CHOICE   0.194 0.096 0.201  0.228  1.000                   
## PROF     0.426 0.248 0.228  0.280  0.356 1.000             
## BRAND    0.268 0.106 0.267  0.321  0.270 0.361 1.000       
## FRENCH   0.111 0.343 0.111  0.093  0.051 0.134 0.104  1.000

2.3.2.3 Modification indices

arrange(modificationindices(CFA_fit_img_7f),-mi)

##          lhs op  rhs     mi    epc sepc.lv sepc.all sepc.nox
## 1      BRAND =~ Im13 23.832  0.220   0.265    0.220    0.220
## 2       Im11 ~~ Im13 21.323 -0.191  -0.191   -0.338   -0.338
## 3      BRAND =~ Im12 17.245 -0.179  -0.216   -0.190   -0.190
## 4       Im21 ~~ Im22 15.139 -0.285  -0.285   -0.455   -0.455
## 5     CHOICE =~ Im20 14.777 -0.151  -0.197   -0.132   -0.132
## 6     CHOICE =~ Im13 13.970  0.133   0.174    0.144    0.144
## 7       Im11 ~~ Im12 13.307  0.145   0.145    0.288    0.288
## 8       FOOD =~ Im11 12.742  0.215   0.174    0.152    0.152
## 9       Im20 ~~ Im21 11.455  0.228   0.228    0.335    0.335
## 10     ATMOS =~ Im12 10.952 -0.115  -0.145   -0.127   -0.127
## 11      Im13 ~~  Im1 10.707  0.068   0.068    0.409    0.409
## 12    CHOICE =~ Im12 10.663 -0.111  -0.145   -0.127   -0.127
## 13      Im13 ~~ Im17  9.392  0.068   0.068    0.355    0.355
## 14       Im4 ~~ Im17  9.096 -0.046  -0.046   -0.446   -0.446
## 15     BRAND =~ Im20  8.230 -0.133  -0.160   -0.107   -0.107
## 16      Im10 ~~ Im16  7.956  0.046   0.046    0.175    0.175
## 17     BRAND =~ Im22  7.656  0.131   0.158    0.103    0.103
## 18    FRENCH =~ Im22  7.278  0.136   0.132    0.087    0.087
## 19     ATMOS =~ Im11  6.691  0.101   0.128    0.112    0.112
## 20      Im22 ~~ Im12  6.644 -0.076  -0.076   -0.185   -0.185
## 21    CHOICE =~  Im5  6.302  0.086   0.112    0.084    0.084
## 22     BRAND =~  Im4  6.247 -0.067  -0.081   -0.060   -0.060
## 23  PRODQUAL =~  Im5  6.120  0.171   0.120    0.091    0.091
## 24      Im14 ~~ Im16  6.048 -0.039  -0.039   -0.191   -0.191
## 25      Im10 ~~  Im6  6.011 -0.035  -0.035   -0.147   -0.147
## 26     BRAND =~  Im5  5.755  0.095   0.115    0.086    0.086
## 27       Im3 ~~  Im1  5.614 -0.034  -0.034   -0.281   -0.281
## 28      DECO =~  Im7  5.531 -0.093  -0.114   -0.095   -0.095
## 29      DECO =~  Im6  5.531  0.078   0.097    0.080    0.080
## 30     ATMOS =~  Im5  5.517  0.089   0.113    0.085    0.085
## 31      DECO =~ Im18  5.361  0.099   0.123    0.088    0.088
## 32      DECO =~ Im17  5.361 -0.100  -0.124   -0.099   -0.099
## 33    FRENCH =~ Im20  5.231 -0.113  -0.111   -0.074   -0.074
## 34      Im22 ~~ Im11  5.182  0.087   0.087    0.131    0.131
## 35      FOOD =~ Im13  5.137 -0.127  -0.103   -0.086   -0.086
## 36       Im3 ~~  Im4  5.131  0.162   0.162    1.061    1.061
## 37      DECO =~ Im20  5.124 -0.096  -0.118   -0.079   -0.079
## 38     BRAND =~  Im7  5.064 -0.090  -0.108   -0.089   -0.089
## 39     BRAND =~  Im6  5.064  0.076   0.091    0.076    0.076
## 40      Im22 ~~  Im1  5.051  0.056   0.056    0.290    0.290
## 41      Im13 ~~ Im16  5.040 -0.067  -0.067   -0.138   -0.138
## 42      Im11 ~~  Im6  4.965 -0.069  -0.069   -0.109   -0.109
## 43      Im10 ~~ Im13  4.793 -0.031  -0.031   -0.146   -0.146
## 44       Im4 ~~ Im18  4.776  0.040   0.040    0.166    0.166
## 45       Im5 ~~  Im6  4.758 -0.065  -0.065   -0.108   -0.108
## 46       Im3 ~~ Im22  4.749  0.049   0.049    0.143    0.143
## 47      Im10 ~~  Im7  4.706  0.032   0.032    0.265    0.265
## 48    CHOICE =~ Im22  4.697  0.087   0.113    0.074    0.074
## 49       Im3 ~~  Im5  4.674 -0.071  -0.071   -0.178   -0.178
## 50      Im13 ~~  Im2  4.562 -0.044  -0.044   -0.125   -0.125
## 51      FOOD =~  Im5  4.520  0.117   0.095    0.072    0.072
## 52      Im20 ~~ Im17  4.488 -0.057  -0.057   -0.230   -0.230
## 53     ATMOS =~  Im4  4.309 -0.052  -0.066   -0.049   -0.049
## 54      DECO =~ Im22  4.302  0.090   0.111    0.072    0.072
## 55      PROF =~  Im2  4.223  0.170   0.157    0.122    0.122
## 56      PROF =~  Im1  4.223 -0.192  -0.177   -0.133   -0.133
## 57      Im20 ~~  Im6  4.215 -0.064  -0.064   -0.115   -0.115
## 58  PRODQUAL =~  Im1  4.027  0.145   0.102    0.077    0.077
## 59  PRODQUAL =~  Im2  4.027 -0.129  -0.090   -0.070   -0.070
## 60      PROF =~ Im12  3.965 -0.117  -0.108   -0.095   -0.095
## 61      Im14 ~~  Im6  3.823  0.027   0.027    0.149    0.149
## 62      FOOD =~  Im6  3.804 -0.271  -0.220   -0.183   -0.183
## 63      FOOD =~  Im7  3.804  0.321   0.260    0.215    0.215
## 64       Im2 ~~ Im17  3.691  0.033   0.033    0.192    0.192
## 65       Im4 ~~  Im6  3.588  0.033   0.033    0.143    0.143
## 66       Im3 ~~ Im17  3.342  0.028   0.028    0.198    0.198
## 67      Im11 ~~  Im1  3.335 -0.045  -0.045   -0.189   -0.189
## 68       Im5 ~~  Im1  3.275  0.043   0.043    0.188    0.188
## 69      PROF =~ Im20  3.209 -0.113  -0.104   -0.069   -0.069
## 70    CHOICE =~ Im21  3.202  0.067   0.087    0.064    0.064
## 71       Im3 ~~  Im2  3.151  0.026   0.026    0.100    0.100
## 72      Im20 ~~ Im13  3.089  0.055   0.055    0.111    0.111
## 73      Im18 ~~  Im6  3.067  0.046   0.046    0.091    0.091
## 74      Im14 ~~  Im7  3.014 -0.026  -0.026   -0.272   -0.272
## 75      Im11 ~~ Im17  2.983 -0.045  -0.045   -0.163   -0.163
## 76    FRENCH =~ Im11  2.967  0.080   0.078    0.069    0.069
## 77     ATMOS =~ Im13  2.904  0.062   0.078    0.065    0.065
## 78       Im5 ~~  Im7  2.807  0.048   0.048    0.154    0.154
## 79      Im10 ~~ Im11  2.784  0.028   0.028    0.093    0.093
## 80      Im20 ~~  Im1  2.774 -0.042  -0.042   -0.198   -0.198
## 81       Im5 ~~ Im14  2.721  0.026   0.026    0.115    0.115
## 82       Im1 ~~ Im17  2.656 -0.029  -0.029   -0.359   -0.359
## 83    FRENCH =~ Im19  2.578  0.085   0.083    0.074    0.074
## 84    FRENCH =~ Im16  2.578 -0.082  -0.080   -0.066   -0.066
## 85       Im2 ~~ Im16  2.577  0.038   0.038    0.088    0.088
## 86    CHOICE =~ Im14  2.577  0.027   0.035    0.041    0.041
## 87    CHOICE =~ Im10  2.577 -0.026  -0.035   -0.039   -0.039
## 88      Im21 ~~ Im18  2.573 -0.052  -0.052   -0.084   -0.084
## 89       Im4 ~~ Im11  2.457 -0.034  -0.034   -0.113   -0.113
## 90      PROF =~ Im13  2.455  0.096   0.089    0.074    0.074
## 91      Im22 ~~ Im19  2.419 -0.049  -0.049   -0.115   -0.115
## 92       Im4 ~~ Im22  2.418 -0.034  -0.034   -0.138   -0.138
## 93       Im3 ~~ Im20  2.350 -0.034  -0.034   -0.093   -0.093
## 94      Im12 ~~  Im7  2.333  0.036   0.036    0.178    0.178
## 95      DECO =~ Im12  2.244 -0.054  -0.066   -0.058   -0.058
## 96      Im11 ~~  Im7  2.221  0.044   0.044    0.137    0.137
## 97      Im19 ~~ Im17  2.187  0.035   0.035    0.193    0.193
## 98  PRODQUAL =~ Im16  2.157 -0.133  -0.094   -0.078   -0.078
## 99  PRODQUAL =~ Im19  2.157  0.140   0.098    0.087    0.087
## 100     Im10 ~~ Im17  2.035 -0.017  -0.017   -0.161   -0.161
## 101     Im14 ~~ Im17  1.988  0.016   0.016    0.201    0.201
## 102      Im4 ~~  Im1  1.978  0.020   0.020    0.227    0.227
## 103      Im3 ~~ Im12  1.906 -0.024  -0.024   -0.092   -0.092
## 104     Im12 ~~  Im6  1.902 -0.033  -0.033   -0.084   -0.084
## 105   CHOICE =~ Im16  1.817  0.068   0.089    0.074    0.074
## 106   CHOICE =~ Im19  1.817 -0.071  -0.093   -0.083   -0.083
## 107     Im14 ~~  Im2  1.800  0.015   0.015    0.098    0.098
## 108     Im18 ~~  Im7  1.743 -0.033  -0.033   -0.128   -0.128
## 109   FRENCH =~  Im5  1.735  0.059   0.057    0.043    0.043
## 110     Im11 ~~  Im2  1.713  0.033   0.033    0.064    0.064
## 111    ATMOS =~ Im17  1.684 -0.057  -0.073   -0.058   -0.058
## 112    ATMOS =~ Im18  1.684  0.057   0.072    0.052    0.052
## 113     Im19 ~~ Im18  1.680 -0.034  -0.034   -0.082   -0.082
## 114    BRAND =~  Im3  1.663  0.034   0.041    0.031    0.031
## 115      Im3 ~~ Im14  1.662 -0.012  -0.012   -0.102   -0.102
## 116   FRENCH =~  Im2  1.647  0.039   0.038    0.030    0.030
## 117   FRENCH =~  Im1  1.647 -0.045  -0.043   -0.033   -0.033
## 118     Im22 ~~  Im2  1.646 -0.032  -0.032   -0.077   -0.077
## 119     Im22 ~~ Im18  1.613  0.041   0.041    0.077    0.077
## 120     FOOD =~  Im2  1.604  0.050   0.040    0.031    0.031
## 121     FOOD =~  Im1  1.604 -0.056  -0.046   -0.034   -0.034
## 122 PRODQUAL =~  Im4  1.602 -0.058  -0.041   -0.030   -0.030
## 123     Im22 ~~ Im13  1.588 -0.040  -0.040   -0.086   -0.086
## 124      Im4 ~~  Im2  1.557 -0.018  -0.018   -0.095   -0.095
## 125     Im14 ~~ Im21  1.552  0.021   0.021    0.091    0.091
## 126      Im5 ~~ Im16  1.529 -0.043  -0.043   -0.064   -0.064
## 127     Im12 ~~ Im17  1.526 -0.026  -0.026   -0.151   -0.151
## 128     Im10 ~~ Im18  1.519  0.018   0.018    0.072    0.072
## 129 PRODQUAL =~ Im22  1.519 -0.095  -0.067   -0.044   -0.044
## 130      Im2 ~~ Im18  1.481 -0.026  -0.026   -0.063   -0.063
## 131     Im12 ~~ Im13  1.475  0.089   0.089    0.257    0.257
## 132 PRODQUAL =~  Im6  1.473 -0.073  -0.052   -0.043   -0.043
## 133 PRODQUAL =~  Im7  1.473  0.087   0.061    0.051    0.051
## 134     Im14 ~~ Im18  1.464 -0.017  -0.017   -0.088   -0.088
## 135     PROF =~ Im22  1.445  0.077   0.071    0.047    0.047
## 136     DECO =~ Im13  1.431  0.045   0.055    0.046    0.046
## 137 PRODQUAL =~ Im17  1.422  0.109   0.076    0.062    0.062
## 138 PRODQUAL =~ Im18  1.422 -0.108  -0.076   -0.054   -0.054
## 139      Im4 ~~ Im12  1.373  0.019   0.019    0.106    0.106
## 140    ATMOS =~  Im1  1.355  0.043   0.054    0.040    0.040
## 141    ATMOS =~  Im2  1.355 -0.038  -0.048   -0.037   -0.037
## 142     Im22 ~~  Im7  1.342  0.035   0.035    0.133    0.133
## 143      Im3 ~~ Im18  1.316 -0.022  -0.022   -0.065   -0.065
## 144      Im3 ~~ Im11  1.290  0.025   0.025    0.061    0.061
## 145     PROF =~  Im4  1.267 -0.055  -0.050   -0.037   -0.037
## 146     Im13 ~~ Im19  1.244  0.029   0.029    0.080    0.080
## 147      Im3 ~~ Im10  1.231  0.011   0.011    0.071    0.071
## 148     Im10 ~~ Im12  1.205  0.014   0.014    0.077    0.077
## 149     Im12 ~~ Im16  1.199  0.030   0.030    0.071    0.071
## 150    BRAND =~ Im11  1.070 -0.047  -0.056   -0.049   -0.049
## 151    BRAND =~  Im2  1.067  0.042   0.051    0.039    0.039
## 152    BRAND =~  Im1  1.067 -0.048  -0.057   -0.043   -0.043
## 153     Im14 ~~ Im12  1.061 -0.013  -0.013   -0.090   -0.090
## 154      Im4 ~~  Im7  1.054 -0.017  -0.017   -0.147   -0.147
## 155 PRODQUAL =~ Im20  1.037  0.077   0.054    0.036    0.036
## 156     Im21 ~~ Im17  1.017  0.027   0.027    0.101    0.101
## 157     Im20 ~~ Im19  0.988  0.031   0.031    0.068    0.068
## 158     PROF =~ Im17  0.986  0.084   0.077    0.062    0.062
## 159     PROF =~ Im18  0.986 -0.083  -0.077   -0.055   -0.055
## 160     Im19 ~~  Im7  0.949  0.025   0.025    0.122    0.122
## 161     PROF =~  Im7  0.940 -0.060  -0.055   -0.045   -0.045
## 162     PROF =~  Im6  0.940  0.050   0.046    0.039    0.039
## 163     Im13 ~~ Im18  0.925 -0.026  -0.026   -0.057   -0.057
## 164      Im5 ~~  Im2  0.918 -0.023  -0.023   -0.047   -0.047
## 165     Im14 ~~ Im13  0.889  0.013   0.013    0.079    0.079
## 166     Im16 ~~  Im7  0.880 -0.027  -0.027   -0.097   -0.097
## 167      Im1 ~~ Im18  0.847  0.019   0.019    0.101    0.101
## 168    ATMOS =~  Im3  0.826  0.022   0.028    0.022    0.022
## 169     FOOD =~ Im20  0.814 -0.052  -0.042   -0.028   -0.028
## 170     Im22 ~~  Im6  0.806  0.028   0.028    0.054    0.054
## 171      Im5 ~~ Im19  0.786 -0.026  -0.026   -0.052   -0.052
## 172    BRAND =~ Im16  0.775 -0.050  -0.060   -0.050   -0.050
## 173    BRAND =~ Im19  0.775  0.052   0.063    0.056    0.056
## 174      Im3 ~~ Im19  0.774  0.016   0.016    0.061    0.061
## 175    BRAND =~ Im14  0.773  0.017   0.020    0.023    0.023
## 176    BRAND =~ Im10  0.773 -0.016  -0.020   -0.022   -0.022
## 177     Im10 ~~ Im19  0.726 -0.012  -0.012   -0.062   -0.062
## 178   FRENCH =~ Im13  0.706 -0.035  -0.034   -0.028   -0.028
## 179     PROF =~  Im5  0.688  0.055   0.051    0.038    0.038
## 180      Im4 ~~  Im5  0.687  0.029   0.029    0.103    0.103
## 181     Im20 ~~ Im12  0.675  0.024   0.024    0.054    0.054
## 182      Im2 ~~  Im7  0.669  0.016   0.016    0.079    0.079
## 183      Im3 ~~  Im7  0.637 -0.014  -0.014   -0.084   -0.084
## 184 PRODQUAL =~ Im14  0.619  0.031   0.022    0.025    0.025
## 185 PRODQUAL =~ Im10  0.619 -0.030  -0.021   -0.024   -0.024
## 186     Im21 ~~  Im7  0.611 -0.023  -0.023   -0.076   -0.076
## 187      Im5 ~~ Im22  0.596  0.028   0.028    0.044    0.044
## 188      Im4 ~~ Im10  0.595 -0.007  -0.007   -0.066   -0.066
## 189     Im20 ~~ Im18  0.582  0.025   0.025    0.043    0.043
## 190     Im10 ~~  Im2  0.581 -0.008  -0.008   -0.045   -0.045
## 191      Im4 ~~ Im16  0.579  0.016   0.016    0.062    0.062
## 192     Im21 ~~  Im2  0.574  0.019   0.019    0.039    0.039
## 193     Im10 ~~ Im21  0.544 -0.013  -0.013   -0.043   -0.043
## 194     Im14 ~~ Im22  0.525 -0.012  -0.012   -0.062   -0.062
## 195     Im13 ~~  Im7  0.518 -0.018  -0.018   -0.080   -0.080
## 196      Im5 ~~ Im11  0.501  0.026   0.026    0.033    0.033
## 197     Im20 ~~ Im11  0.498  0.027   0.027    0.038    0.038
## 198     Im12 ~~  Im2  0.492 -0.013  -0.013   -0.043   -0.043
## 199     Im11 ~~ Im18  0.492  0.023   0.023    0.035    0.035
## 200   CHOICE =~  Im3  0.483 -0.015  -0.020   -0.015   -0.015
## 201      Im1 ~~ Im16  0.483 -0.017  -0.017   -0.082   -0.082
## 202     Im21 ~~ Im12  0.479  0.020   0.020    0.043    0.043
## 203      Im5 ~~ Im10  0.474 -0.011  -0.011   -0.039   -0.039
## 204   CHOICE =~ Im11  0.473 -0.026  -0.034   -0.030   -0.030
## 205     Im10 ~~ Im20  0.466  0.012   0.012    0.043    0.043
## 206     PROF =~  Im3  0.453  0.032   0.029    0.022    0.022
## 207   FRENCH =~  Im3  0.431 -0.019  -0.018   -0.014   -0.014
## 208     FOOD =~  Im3  0.430 -0.023  -0.019   -0.014   -0.014
## 209     FOOD =~ Im19  0.429  0.047   0.038    0.034    0.034
## 210     FOOD =~ Im16  0.429 -0.045  -0.037   -0.031   -0.031
## 211     PROF =~ Im11  0.410  0.039   0.036    0.032    0.032
## 212      Im5 ~~ Im20  0.382  0.023   0.023    0.033    0.033
## 213     Im13 ~~  Im6  0.377  0.016   0.016    0.036    0.036
## 214     Im14 ~~ Im19  0.372  0.009   0.009    0.056    0.056
## 215     Im21 ~~ Im13  0.372 -0.019  -0.019   -0.036   -0.036
## 216     PROF =~ Im21  0.371  0.036   0.033    0.024    0.024
## 217   CHOICE =~  Im4  0.369 -0.014  -0.018   -0.013   -0.013
## 218     Im22 ~~ Im17  0.360  0.016   0.016    0.071    0.071
## 219   FRENCH =~ Im21  0.360 -0.029  -0.028   -0.020   -0.020
## 220     Im21 ~~ Im11  0.346 -0.022  -0.022   -0.029   -0.029
## 221      Im5 ~~ Im17  0.345  0.015   0.015    0.055    0.055
## 222     Im14 ~~ Im20  0.330 -0.010  -0.010   -0.045   -0.045
## 223     FOOD =~ Im21  0.320  0.032   0.026    0.019    0.019
## 224   CHOICE =~ Im17  0.309  0.023   0.030    0.024    0.024
## 225   CHOICE =~ Im18  0.309 -0.023  -0.030   -0.021   -0.021
## 226      Im3 ~~ Im13  0.299  0.010   0.010    0.035    0.035
## 227      Im4 ~~ Im19  0.281 -0.010  -0.010   -0.050   -0.050
## 228     Im22 ~~ Im16  0.277  0.019   0.019    0.033    0.033
## 229      Im5 ~~ Im21  0.277 -0.019  -0.019   -0.026   -0.026
## 230      Im4 ~~ Im14  0.246  0.005   0.005    0.053    0.053
## 231     DECO =~ Im11  0.238  0.019   0.024    0.021    0.021
## 232     Im16 ~~ Im18  0.231 -0.015  -0.015   -0.026   -0.026
## 233     Im17 ~~  Im7  0.228 -0.010  -0.010   -0.094   -0.094
## 234     Im21 ~~ Im16  0.227 -0.017  -0.017   -0.026   -0.026
## 235     Im20 ~~ Im22  0.211  0.043   0.043    0.074    0.074
## 236     Im17 ~~  Im6  0.208  0.010   0.010    0.045    0.045
## 237     Im20 ~~  Im2  0.203 -0.011  -0.011   -0.025   -0.025
## 238      Im2 ~~ Im19  0.202 -0.009  -0.009   -0.029   -0.029
## 239     FOOD =~  Im4  0.194 -0.016  -0.013   -0.010   -0.010
## 240      Im4 ~~ Im13  0.168 -0.007  -0.007   -0.035   -0.035
## 241     Im14 ~~ Im11  0.165  0.007   0.007    0.028    0.028
## 242     FOOD =~ Im22  0.151  0.023   0.018    0.012    0.012
## 243     Im12 ~~ Im18  0.146 -0.010  -0.010   -0.024   -0.024
## 244     Im20 ~~ Im16  0.145  0.014   0.014    0.022    0.022
## 245     Im21 ~~  Im1  0.132  0.009   0.009    0.040    0.040
## 246    ATMOS =~ Im19  0.131 -0.017  -0.022   -0.019   -0.019
## 247    ATMOS =~ Im16  0.131  0.016   0.021    0.017    0.017
## 248      Im4 ~~ Im20  0.129  0.008   0.008    0.029    0.029
## 249      Im1 ~~  Im7  0.126 -0.007  -0.007   -0.075   -0.075
## 250     Im12 ~~  Im1  0.110 -0.006  -0.006   -0.044   -0.044
## 251      Im3 ~~  Im6  0.106  0.006   0.006    0.018    0.018
## 252      Im2 ~~  Im6  0.094 -0.006  -0.006   -0.016   -0.016
## 253   FRENCH =~ Im18  0.094  0.013   0.012    0.009    0.009
## 254   FRENCH =~ Im17  0.094 -0.013  -0.013   -0.010   -0.010
## 255     Im10 ~~  Im1  0.093 -0.003  -0.003   -0.038   -0.038
## 256 PRODQUAL =~ Im21  0.088  0.021   0.015    0.011    0.011
## 257      Im5 ~~ Im18  0.083  0.009   0.009    0.014    0.014
## 258     Im20 ~~  Im7  0.082  0.009   0.009    0.030    0.030
## 259     DECO =~  Im2  0.075  0.009   0.011    0.008    0.008
## 260     DECO =~  Im1  0.075 -0.010  -0.012   -0.009   -0.009
## 261      Im5 ~~ Im12  0.067  0.007   0.007    0.015    0.015
## 262     Im14 ~~  Im1  0.063 -0.003  -0.003   -0.039   -0.039
## 263    ATMOS =~ Im14  0.061  0.004   0.006    0.006    0.006
## 264    ATMOS =~ Im10  0.061 -0.004  -0.006   -0.006   -0.006
## 265     Im21 ~~ Im19  0.060  0.008   0.008    0.015    0.015
## 266      Im4 ~~ Im21  0.059  0.005   0.005    0.018    0.018
## 267     PROF =~ Im10  0.058  0.008   0.007    0.008    0.008
## 268     PROF =~ Im14  0.058 -0.008  -0.007   -0.009   -0.009
## 269      Im1 ~~ Im19  0.056 -0.005  -0.005   -0.034   -0.034
## 270   CHOICE =~  Im6  0.055 -0.007  -0.009   -0.007   -0.007
## 271   CHOICE =~  Im7  0.055  0.008   0.010    0.008    0.008
## 272     DECO =~ Im14  0.052  0.005   0.006    0.007    0.007
## 273     DECO =~ Im10  0.052 -0.005  -0.006   -0.006   -0.006
## 274     Im10 ~~ Im22  0.051  0.004   0.004    0.015    0.015
## 275   FRENCH =~ Im12  0.045 -0.008  -0.008   -0.007   -0.007
## 276      Im1 ~~  Im6  0.039 -0.004  -0.004   -0.021   -0.021
## 277    ATMOS =~  Im6  0.036 -0.006  -0.008   -0.007   -0.007
## 278    ATMOS =~  Im7  0.036  0.008   0.010    0.008    0.008
## 279     Im12 ~~ Im19  0.023 -0.004  -0.004   -0.011   -0.011
## 280     DECO =~ Im21  0.016  0.005   0.006    0.005    0.005
## 281     FOOD =~ Im17  0.015  0.006   0.005    0.004    0.004
## 282     FOOD =~ Im18  0.015 -0.006  -0.005   -0.004   -0.004
## 283      Im3 ~~ Im21  0.013 -0.003  -0.003   -0.006   -0.006
## 284     Im16 ~~  Im6  0.011 -0.003  -0.003   -0.006   -0.006
## 285     Im19 ~~  Im6  0.009 -0.002  -0.002   -0.006   -0.006
## 286     Im11 ~~ Im19  0.006 -0.002  -0.002   -0.005   -0.005
## 287     Im21 ~~  Im6  0.006  0.002   0.002    0.004    0.004
## 288     DECO =~ Im16  0.004  0.004   0.005    0.004    0.004
## 289     DECO =~ Im19  0.004 -0.004  -0.005   -0.004   -0.004
## 290     Im11 ~~ Im16  0.002  0.002   0.002    0.002    0.002
## 291   FRENCH =~ Im14  0.001  0.001   0.001    0.002    0.002
## 292   FRENCH =~ Im10  0.001 -0.001  -0.001   -0.002   -0.002
## 293      Im3 ~~ Im16  0.001 -0.001  -0.001   -0.002   -0.002
## 294   FRENCH =~  Im4  0.001 -0.001  -0.001    0.000    0.000
## 295     Im16 ~~ Im17  0.000  0.000   0.000    0.002    0.002
## 296 PRODQUAL =~  Im3  0.000  0.000   0.000    0.000    0.000
## 297      Im5 ~~ Im13  0.000  0.000   0.000    0.000    0.000
## 298    BRAND =~ Im21  0.000  0.000   0.000    0.000    0.000
## 299     FOOD =~ Im12  0.000  0.000   0.000    0.000    0.000

2.4 SEM

## don't actually think we need this as we can use the full data for confirmatory and path analysis
# data_img_EFA2
# data.frame(EFA_PAFn[[3]]$scores)
# 
# numcol_data_img_EFA = dim(data_img_EFA2)[2]
# numcol_scores = dim(EFA_PAFn[[3]]$scores)[2]
# numcol_data_img_EFA
# numcol_scores
# 
# CFA_data = cbind(data_img_EFA2, EFA_PAFn[[3]]$scores, survey_excl_img2["SAT_1"])
# CFA_data
# # colnames(CFA_data)[23:29] = c("Gourmet food", "Brand image", "Choice range", "Relaxed atmosphere", "Decoration", "Product quality", "Frenchness")
# 
# # colnames(CFA_data)[numcol_data_img_EFA:(numcol_data_img_EFA + numcol_scores)] = c("FOOD", "BRAND", "CHOICE", "ATMOS", "DECO")
# colnames(CFA_data)[numcol_data_img_EFA:(numcol_data_img_EFA + numcol_scores)] = c("FOOD", "BRAND", "CHOICE", "ATMOS", "DECO", "QUAL", "FRENCH")
# 
# CFA_data

2.4.1 model images to mediators

# missing Im8, Im15, Im9

# model_SEM <- "
# DECO =~ Im3 + Im4 + Im5
# FOOD =~ Im10 + Im14
# ATMOS =~ Im20 + Im21 + Im22
# PRODQUAL =~ Im11 + Im12 + Im13
# CHOICE =~ Im1 + Im2  
# PROF =~ Im16 + Im19
# BRAND =~ Im17 + Im18
# FRENCH =~ Im6 + Im7
# 
# AFCOM =~ COM_A1 + COM_A2 + COM_A3 + COM_A4
# SAT =~ SAT_1 + SAT_2 + SAT_3
# RI =~ C_REP1 + C_REP2 + C_REP3
# COI =~ C_CR1 + C_CR3 + C_CR4
# 
# SAT ~ DECO + FOOD + ATMOS + PRODQUAL + CHOICE + PROF + BRAND + FRENCH + Im8 + Im15 + Im9
# AFCOM ~ DECO + FOOD + ATMOS + PRODQUAL + CHOICE + PROF + BRAND + FRENCH + Im8 + Im15 + Im9
# "

# delete relationships based on regression significance levels
model_SEM <- "
DECO =~ Im3 + Im4 + Im5
FOOD =~ Im10 + Im14
ATMOS =~ Im20 + Im21 + Im22
PRODQUAL =~ Im11 + Im12 + Im13
CHOICE =~ Im1 + Im2  
PROF =~ Im16 + Im19
BRAND =~ Im17 + Im18
FRENCH =~ Im6 + Im7

AFCOM =~ COM_A1 + COM_A2 + COM_A3 + COM_A4
SAT =~ SAT_1 + SAT_2 + SAT_3
RI =~ C_REP1 + C_REP2 + C_REP3
COI =~ C_CR1 + C_CR3 + C_CR4

SAT ~ DECO + CHOICE + PROF
AFCOM ~ ATMOS + PRODQUAL + FRENCH
"

2.4.2 linear regression

# # linear regression
# lm_SAT_1 <-  lm (model_SAT_1, data = survey) 
# summary(lm_SAT_1)
# # note: lm deletes all missing variables in the Xs! (not in Ys) (see help lavOptions)

2.4.3 path analysis

# path analysis
SEM_fit <- cfa(model_SEM, data=survey, missing="ML")
summary(SEM_fit, fit.measures=TRUE, standardized=TRUE)

## lavaan 0.6.15 ended normally after 143 iterations
## 
##   Estimator                                         ML
##   Optimization method                           NLMINB
##   Number of model parameters                       148
## 
##   Number of observations                           553
##   Number of missing patterns                       135
## 
## Model Test User Model:
##                                                       
##   Test statistic                               807.817
##   Degrees of freedom                               412
##   P-value (Chi-square)                           0.000
## 
## Model Test Baseline Model:
## 
##   Test statistic                             11978.557
##   Degrees of freedom                               496
##   P-value                                        0.000
## 
## User Model versus Baseline Model:
## 
##   Comparative Fit Index (CFI)                    0.966
##   Tucker-Lewis Index (TLI)                       0.959
##                                                       
##   Robust Comparative Fit Index (CFI)             0.966
##   Robust Tucker-Lewis Index (TLI)                0.959
## 
## Loglikelihood and Information Criteria:
## 
##   Loglikelihood user model (H0)             -22422.581
##   Loglikelihood unrestricted model (H1)     -22018.673
##                                                       
##   Akaike (AIC)                               45141.162
##   Bayesian (BIC)                             45779.835
##   Sample-size adjusted Bayesian (SABIC)      45310.018
## 
## Root Mean Square Error of Approximation:
## 
##   RMSEA                                          0.042
##   90 Percent confidence interval - lower         0.037
##   90 Percent confidence interval - upper         0.046
##   P-value H_0: RMSEA <= 0.050                    0.999
##   P-value H_0: RMSEA >= 0.080                    0.000
##                                                       
##   Robust RMSEA                                   0.042
##   90 Percent confidence interval - lower         0.038
##   90 Percent confidence interval - upper         0.047
##   P-value H_0: Robust RMSEA <= 0.050             0.998
##   P-value H_0: Robust RMSEA >= 0.080             0.000
## 
## Standardized Root Mean Square Residual:
## 
##   SRMR                                           0.059
## 
## Parameter Estimates:
## 
##   Standard errors                             Standard
##   Information                                 Observed
##   Observed information based on                Hessian
## 
## Latent Variables:
##                    Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
##   DECO =~                                                               
##     Im3               1.000                               1.235    0.936
##     Im4               1.057    0.025   42.676    0.000    1.306    0.970
##     Im5               0.818    0.034   23.801    0.000    1.010    0.760
##   FOOD =~                                                               
##     Im10              1.000                               0.810    0.921
##     Im14              1.019    0.036   28.596    0.000    0.826    0.954
##   ATMOS =~                                                              
##     Im20              1.000                               1.253    0.838
##     Im21              0.865    0.041   20.940    0.000    1.084    0.791
##     Im22              1.060    0.046   23.188    0.000    1.327    0.869
##   PRODQUAL =~                                                           
##     Im11              1.000                               0.703    0.615
##     Im12              1.409    0.094   15.045    0.000    0.991    0.872
##     Im13              1.464    0.105   13.957    0.000    1.029    0.855
##   CHOICE =~                                                             
##     Im1               1.000                               1.302    0.978
##     Im2               0.889    0.032   27.907    0.000    1.157    0.900
##   PROF =~                                                               
##     Im16              1.000                               0.911    0.757
##     Im19              1.030    0.056   18.278    0.000    0.938    0.834
##   BRAND =~                                                              
##     Im17              1.000                               1.205    0.970
##     Im18              0.992    0.041   24.147    0.000    1.196    0.856
##   FRENCH =~                                                             
##     Im6               1.000                               0.986    0.822
##     Im7               1.161    0.066   17.619    0.000    1.144    0.945
##   AFCOM =~                                                              
##     COM_A1            1.000                               1.120    0.785
##     COM_A2            1.180    0.056   21.211    0.000    1.321    0.830
##     COM_A3            1.176    0.059   19.829    0.000    1.317    0.816
##     COM_A4            1.297    0.063   20.613    0.000    1.453    0.845
##   SAT =~                                                                
##     SAT_1             1.000                               0.868    0.859
##     SAT_2             0.937    0.049   19.036    0.000    0.814    0.818
##     SAT_3             0.812    0.055   14.799    0.000    0.705    0.620
##   RI =~                                                                 
##     C_REP1            1.000                               0.588    0.798
##     C_REP2            1.021    0.047   21.905    0.000    0.601    0.955
##     C_REP3            0.719    0.038   19.135    0.000    0.423    0.758
##   COI =~                                                                
##     C_CR1             1.000                               1.641    0.848
##     C_CR3             1.033    0.051   20.134    0.000    1.695    0.822
##     C_CR4             0.967    0.049   19.687    0.000    1.587    0.805
## 
## Regressions:
##                    Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
##   SAT ~                                                                 
##     DECO             -0.107    0.046   -2.357    0.018   -0.153   -0.153
##     CHOICE            0.095    0.040    2.379    0.017    0.142    0.142
##     PROF              0.615    0.090    6.808    0.000    0.645    0.645
##   AFCOM ~                                                               
##     ATMOS             0.437    0.047    9.282    0.000    0.489    0.489
##     PRODQUAL         -0.037    0.076   -0.485    0.628   -0.023   -0.023
##     FRENCH            0.206    0.051    4.031    0.000    0.182    0.182
## 
## Covariances:
##                    Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
##   DECO ~~                                                               
##     FOOD              0.416    0.050    8.380    0.000    0.416    0.416
##     ATMOS             0.730    0.081    8.972    0.000    0.472    0.472
##     PRODQUAL          0.408    0.051    8.031    0.000    0.470    0.470
##     CHOICE            0.709    0.079    9.024    0.000    0.441    0.441
##     PROF              0.750    0.070   10.690    0.000    0.667    0.667
##     BRAND             0.768    0.076   10.124    0.000    0.516    0.516
##     FRENCH            0.412    0.063    6.494    0.000    0.338    0.338
##     RI                0.181    0.035    5.193    0.000    0.249    0.249
##     COI               0.047    0.095    0.492    0.623    0.023    0.023
##   FOOD ~~                                                               
##     ATMOS             0.303    0.050    6.019    0.000    0.299    0.299
##     PRODQUAL          0.257    0.034    7.652    0.000    0.452    0.452
##     CHOICE            0.328    0.050    6.606    0.000    0.311    0.311
##     PROF              0.387    0.043    8.999    0.000    0.525    0.525
##     BRAND             0.317    0.047    6.798    0.000    0.325    0.325
##     FRENCH            0.469    0.047   10.016    0.000    0.588    0.588
##     RI                0.123    0.023    5.283    0.000    0.258    0.258
##     COI              -0.044    0.063   -0.700    0.484   -0.033   -0.033
##   ATMOS ~~                                                              
##     PRODQUAL          0.370    0.053    7.026    0.000    0.420    0.420
##     CHOICE            0.748    0.084    8.879    0.000    0.458    0.458
##     PROF              0.580    0.068    8.542    0.000    0.508    0.508
##     BRAND             0.785    0.080    9.748    0.000    0.520    0.520
##     FRENCH            0.411    0.065    6.374    0.000    0.333    0.333
##     RI                0.281    0.040    7.034    0.000    0.381    0.381
##     COI               0.436    0.103    4.210    0.000    0.212    0.212
##   PRODQUAL ~~                                                           
##     CHOICE            0.437    0.054    8.146    0.000    0.477    0.477
##     PROF              0.348    0.043    8.092    0.000    0.543    0.543
##     BRAND             0.479    0.053    9.046    0.000    0.566    0.566
##     FRENCH            0.211    0.038    5.621    0.000    0.305    0.305
##     RI                0.112    0.022    5.128    0.000    0.270    0.270
##     COI               0.060    0.058    1.036    0.300    0.052    0.052
##   CHOICE ~~                                                             
##     PROF              0.725    0.071   10.200    0.000    0.611    0.611
##     BRAND             0.816    0.079   10.366    0.000    0.520    0.520
##     FRENCH            0.296    0.061    4.829    0.000    0.231    0.231
##     RI                0.216    0.037    5.829    0.000    0.282    0.282
##     COI               0.068    0.100    0.678    0.498    0.032    0.032
##   PROF ~~                                                               
##     BRAND             0.676    0.065   10.326    0.000    0.616    0.616
##     FRENCH            0.363    0.052    6.990    0.000    0.404    0.404
##     RI                0.200    0.030    6.678    0.000    0.373    0.373
##     COI              -0.079    0.077   -1.029    0.304   -0.053   -0.053
##   BRAND ~~                                                              
##     FRENCH            0.388    0.061    6.333    0.000    0.327    0.327
##     RI                0.188    0.034    5.501    0.000    0.265    0.265
##     COI               0.111    0.094    1.190    0.234    0.056    0.056
##   FRENCH ~~                                                             
##     RI                0.134    0.029    4.535    0.000    0.230    0.230
##     COI               0.004    0.078    0.051    0.959    0.002    0.002
##   RI ~~                                                                 
##     COI               0.078    0.047    1.677    0.094    0.081    0.081
##  .AFCOM ~~                                                              
##    .SAT               0.218    0.037    5.825    0.000    0.357    0.357
## 
## Intercepts:
##                    Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
##    .Im3               4.995    0.056   88.576    0.000    4.995    3.787
##    .Im4               4.999    0.057   86.999    0.000    4.999    3.713
##    .Im5               5.036    0.057   87.853    0.000    5.036    3.787
##    .Im10              6.100    0.037  162.781    0.000    6.100    6.936
##    .Im14              6.138    0.037  165.851    0.000    6.138    7.093
##    .Im20              4.672    0.064   73.228    0.000    4.672    3.125
##    .Im21              5.139    0.058   87.975    0.000    5.139    3.750
##    .Im22              4.280    0.065   65.485    0.000    4.280    2.802
##    .Im11              5.654    0.049  115.283    0.000    5.654    4.943
##    .Im12              5.666    0.049  116.116    0.000    5.666    4.985
##    .Im13              5.448    0.052  105.654    0.000    5.448    4.526
##    .Im1               4.792    0.057   84.287    0.000    4.792    3.600
##    .Im2               4.858    0.055   88.415    0.000    4.858    3.781
##    .Im16              5.135    0.052   99.179    0.000    5.135    4.269
##    .Im19              5.146    0.048  107.001    0.000    5.146    4.575
##    .Im17              5.025    0.053   94.560    0.000    5.025    4.043
##    .Im18              4.595    0.060   76.466    0.000    4.595    3.288
##    .Im6               5.827    0.051  113.792    0.000    5.827    4.858
##    .Im7               5.753    0.052  110.790    0.000    5.753    4.754
##    .COM_A1            4.287    0.061   70.288    0.000    4.287    3.007
##    .COM_A2            3.887    0.068   57.199    0.000    3.887    2.443
##    .COM_A3            3.542    0.069   51.223    0.000    3.542    2.194
##    .COM_A4            3.458    0.073   47.108    0.000    3.458    2.010
##    .SAT_1             5.343    0.043  124.118    0.000    5.343    5.289
##    .SAT_2             5.483    0.042  129.018    0.000    5.483    5.510
##    .SAT_3             5.458    0.050  109.971    0.000    5.458    4.798
##    .C_REP1            4.283    0.031  136.277    0.000    4.283    5.807
##    .C_REP2            4.507    0.027  167.674    0.000    4.507    7.164
##    .C_REP3            4.676    0.024  195.449    0.000    4.676    8.380
##    .C_CR1             2.679    0.083   32.285    0.000    2.679    1.384
##    .C_CR3             3.261    0.088   37.105    0.000    3.261    1.582
##    .C_CR4             2.786    0.084   33.092    0.000    2.786    1.414
##     DECO              0.000                               0.000    0.000
##     FOOD              0.000                               0.000    0.000
##     ATMOS             0.000                               0.000    0.000
##     PRODQUAL          0.000                               0.000    0.000
##     CHOICE            0.000                               0.000    0.000
##     PROF              0.000                               0.000    0.000
##     BRAND             0.000                               0.000    0.000
##     FRENCH            0.000                               0.000    0.000
##    .AFCOM             0.000                               0.000    0.000
##    .SAT               0.000                               0.000    0.000
##     RI                0.000                               0.000    0.000
##     COI               0.000                               0.000    0.000
## 
## Variances:
##                    Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
##    .Im3               0.214    0.024    8.767    0.000    0.214    0.123
##    .Im4               0.108    0.024    4.461    0.000    0.108    0.059
##    .Im5               0.747    0.049   15.220    0.000    0.747    0.423
##    .Im10              0.117    0.019    6.135    0.000    0.117    0.151
##    .Im14              0.067    0.019    3.559    0.000    0.067    0.089
##    .Im20              0.666    0.059   11.280    0.000    0.666    0.298
##    .Im21              0.703    0.055   12.679    0.000    0.703    0.374
##    .Im22              0.571    0.060    9.496    0.000    0.571    0.245
##    .Im11              0.814    0.055   14.788    0.000    0.814    0.622
##    .Im12              0.310    0.040    7.841    0.000    0.310    0.240
##    .Im13              0.390    0.045    8.730    0.000    0.390    0.269
##    .Im1               0.076    0.048    1.598    0.110    0.076    0.043
##    .Im2               0.312    0.042    7.417    0.000    0.312    0.189
##    .Im16              0.618    0.051   12.116    0.000    0.618    0.427
##    .Im19              0.385    0.045    8.653    0.000    0.385    0.304
##    .Im17              0.093    0.045    2.055    0.040    0.093    0.060
##    .Im18              0.524    0.055    9.587    0.000    0.524    0.268
##    .Im6               0.468    0.054    8.714    0.000    0.468    0.325
##    .Im7               0.155    0.062    2.520    0.012    0.155    0.106
##    .COM_A1            0.779    0.060   13.036    0.000    0.779    0.383
##    .COM_A2            0.787    0.067   11.838    0.000    0.787    0.311
##    .COM_A3            0.872    0.070   12.387    0.000    0.872    0.335
##    .COM_A4            0.849    0.075   11.385    0.000    0.849    0.287
##    .SAT_1             0.267    0.034    7.920    0.000    0.267    0.262
##    .SAT_2             0.328    0.033    9.901    0.000    0.328    0.331
##    .SAT_3             0.797    0.056   14.318    0.000    0.797    0.616
##    .C_REP1            0.198    0.016   12.178    0.000    0.198    0.364
##    .C_REP2            0.035    0.011    3.224    0.001    0.035    0.089
##    .C_REP3            0.133    0.009   14.064    0.000    0.133    0.426
##    .C_CR1             1.054    0.114    9.275    0.000    1.054    0.281
##    .C_CR3             1.375    0.131   10.514    0.000    1.375    0.324
##    .C_CR4             1.366    0.123   11.130    0.000    1.366    0.352
##     DECO              1.526    0.107   14.317    0.000    1.000    1.000
##     FOOD              0.657    0.049   13.302    0.000    1.000    1.000
##     ATMOS             1.569    0.135   11.580    0.000    1.000    1.000
##     PRODQUAL          0.494    0.067    7.362    0.000    1.000    1.000
##     CHOICE            1.696    0.117   14.476    0.000    1.000    1.000
##     PROF              0.829    0.086    9.605    0.000    1.000    1.000
##     BRAND             1.452    0.104   14.014    0.000    1.000    1.000
##     FRENCH            0.971    0.094   10.349    0.000    1.000    1.000
##    .AFCOM             0.854    0.086    9.878    0.000    0.681    0.681
##    .SAT               0.436    0.050    8.755    0.000    0.579    0.579
##     RI                0.346    0.032   10.668    0.000    1.000    1.000
##     COI               2.693    0.238   11.334    0.000    1.000    1.000

# note: cfa deletes all missing variables in the Xs! (not in Ys) (see help lavOptions)

2.4.3.1 Discussion of global fit measures

Chi square: p-value > 0.05

RMSEA RMSEA <= 0.05 Good fit 0.05 < RMSEA <= 0.08 Acceptable fit 0.08 < RMSEA <= 0.10 Bad fit RMSEA > 0.1 Unacceptable fit

CFI CFI < 0.90 definitely reject model 0.90 < CFI < 0.95 high underrejection rates for misspecified models CFI > 0.95 accept model

2.4.3.2 local fit measures

# semPaths(SEM_fit, what = "path", whatLabels = "std", style = "mx",
#          rotation = 2, layout = "tree3", mar = c(1, 2, 1, 2),
#          nCharNodes = 7,shapeMan = "rectangle", sizeMan = 8, sizeMan2 = 5,
#          curvePivot=TRUE, edge.label.cex = 1.2, edge.color = "skyblue4")


semPaths(SEM_fit, what = "col", whatLabels = "par", style = "ram",
         rotation = 2, layout = "tree3",
         mar = c(1, 2, 1, 2), #margins
         nCharNodes = 7,
         shapeMan = "rectangle", # variable shape
         sizeMan = 4, # variable shape size
         sizeMan2 = 3, # variable shape vertical stretch
         # structural = T, # don't plot image variables (manifests)
         sizeInt = 1, # intercept size
         intercepts = F, # don't include intercepts
         sizeLat = 5, #factor size
         asize = 2, # arrow size
         curvePivot=T, # edge broken curve
         edge.label.cex = .5, # edge label size
         # edge.color = "skyblue4",
         # levels= c(1,2,7,8,9,10),
         groups = "latents",
         cut = .5 #cutoff for edges,
         )

# semPaths(SEM_fit, what = "est", whatLabels = "std", style = "mx",
#          rotation = 2, layout = "tree3", 
#          mar = c(1, 2, 1, 2), #margins
#          nCharNodes = 7,
#          shapeMan = "rectangle", # variable shape
#          sizeMan = 4, # variable shape size
#          sizeMan2 = 3, # variable shape vertical stretch
#          structural = T, # don't plot image variables (manifests)
#          sizeInt = 1, # intercept size
#          intercepts = F, # don't include intercepts
#          sizeLat = 5, #factor size
#          asize = 2, # arrow size
#          curvePivot=T, # edge broken curve
#          edge.label.cex = .6, # edge label size
#          edge.color = "skyblue4",
#          # levels= c(1,2,7,8,9,10),
#          # groups = "latents",
#          cut = .4 #cutoff for edges,
#          )

lambda = inspect(SEM_fit, what="std")$lambda
theta = inspect(SEM_fit, what="std")$theta

# create lambda matrix with ones instead of std.all
ones <- lambda
ones[ones>0] <- 1

# a matrix with dimensions of lambda matrix but with lambdas replaced by thetas
theta_lb <- theta %*% ones

2.4.3.2.1 Indicator reliability criterion (Individual Item Reliability)

# JONATHAN
# calculate indicator reliabilities (should be larger than 0.4)
indicrel <- lambda^2/(lambda^2 + theta_lb)
# indicrel

# replace all values satisfying condition with NaN for visibility
indicrel_fail <- indicrel
indicrel_fail[indicrel_fail>.4] <- NaN
indicrel_fail

##        DECO FOOD ATMOS PRODQU CHOICE PROF BRAND FRENCH AFCOM   SAT  RI COI
## Im3     NaN  NaN   NaN    NaN    NaN  NaN   NaN    NaN   NaN   NaN NaN NaN
## Im4     NaN  NaN   NaN    NaN    NaN  NaN   NaN    NaN   NaN   NaN NaN NaN
## Im5     NaN  NaN   NaN    NaN    NaN  NaN   NaN    NaN   NaN   NaN NaN NaN
## Im10    NaN  NaN   NaN    NaN    NaN  NaN   NaN    NaN   NaN   NaN NaN NaN
## Im14    NaN  NaN   NaN    NaN    NaN  NaN   NaN    NaN   NaN   NaN NaN NaN
## Im20    NaN  NaN   NaN    NaN    NaN  NaN   NaN    NaN   NaN   NaN NaN NaN
## Im21    NaN  NaN   NaN    NaN    NaN  NaN   NaN    NaN   NaN   NaN NaN NaN
## Im22    NaN  NaN   NaN    NaN    NaN  NaN   NaN    NaN   NaN   NaN NaN NaN
## Im11    NaN  NaN   NaN  0.378    NaN  NaN   NaN    NaN   NaN   NaN NaN NaN
## Im12    NaN  NaN   NaN    NaN    NaN  NaN   NaN    NaN   NaN   NaN NaN NaN
## Im13    NaN  NaN   NaN    NaN    NaN  NaN   NaN    NaN   NaN   NaN NaN NaN
## Im1     NaN  NaN   NaN    NaN    NaN  NaN   NaN    NaN   NaN   NaN NaN NaN
## Im2     NaN  NaN   NaN    NaN    NaN  NaN   NaN    NaN   NaN   NaN NaN NaN
## Im16    NaN  NaN   NaN    NaN    NaN  NaN   NaN    NaN   NaN   NaN NaN NaN
## Im19    NaN  NaN   NaN    NaN    NaN  NaN   NaN    NaN   NaN   NaN NaN NaN
## Im17    NaN  NaN   NaN    NaN    NaN  NaN   NaN    NaN   NaN   NaN NaN NaN
## Im18    NaN  NaN   NaN    NaN    NaN  NaN   NaN    NaN   NaN   NaN NaN NaN
## Im6     NaN  NaN   NaN    NaN    NaN  NaN   NaN    NaN   NaN   NaN NaN NaN
## Im7     NaN  NaN   NaN    NaN    NaN  NaN   NaN    NaN   NaN   NaN NaN NaN
## COM_A1  NaN  NaN   NaN    NaN    NaN  NaN   NaN    NaN   NaN   NaN NaN NaN
## COM_A2  NaN  NaN   NaN    NaN    NaN  NaN   NaN    NaN   NaN   NaN NaN NaN
## COM_A3  NaN  NaN   NaN    NaN    NaN  NaN   NaN    NaN   NaN   NaN NaN NaN
## COM_A4  NaN  NaN   NaN    NaN    NaN  NaN   NaN    NaN   NaN   NaN NaN NaN
## SAT_1   NaN  NaN   NaN    NaN    NaN  NaN   NaN    NaN   NaN   NaN NaN NaN
## SAT_2   NaN  NaN   NaN    NaN    NaN  NaN   NaN    NaN   NaN   NaN NaN NaN
## SAT_3   NaN  NaN   NaN    NaN    NaN  NaN   NaN    NaN   NaN 0.384 NaN NaN
## C_REP1  NaN  NaN   NaN    NaN    NaN  NaN   NaN    NaN   NaN   NaN NaN NaN
## C_REP2  NaN  NaN   NaN    NaN    NaN  NaN   NaN    NaN   NaN   NaN NaN NaN
## C_REP3  NaN  NaN   NaN    NaN    NaN  NaN   NaN    NaN   NaN   NaN NaN NaN
## C_CR1   NaN  NaN   NaN    NaN    NaN  NaN   NaN    NaN   NaN   NaN NaN NaN
## C_CR3   NaN  NaN   NaN    NaN    NaN  NaN   NaN    NaN   NaN   NaN NaN NaN
## C_CR4   NaN  NaN   NaN    NaN    NaN  NaN   NaN    NaN   NaN   NaN NaN NaN

# FERESHTEH
#Local Fit

std.loadings<- inspect(SEM_fit, what="std")$lambda
check=std.loadings
check[check>0] <- 1
std.loadings[std.loadings==0] <- NA
std.loadings2 <- std.loadings^2
std.theta<- inspect(SEM_fit, what="std")$theta

#Individual item Reliability
IIR=std.loadings2/(colSums(std.theta)+std.loadings2)
IIR

##         DECO  FOOD ATMOS PRODQU CHOICE  PROF BRAND FRENCH AFCOM   SAT    RI
## Im3    0.877    NA    NA     NA     NA    NA    NA     NA    NA    NA    NA
## Im4    0.941    NA    NA     NA     NA    NA    NA     NA    NA    NA    NA
## Im5    0.577    NA    NA     NA     NA    NA    NA     NA    NA    NA    NA
## Im10      NA 0.849    NA     NA     NA    NA    NA     NA    NA    NA    NA
## Im14      NA 0.911    NA     NA     NA    NA    NA     NA    NA    NA    NA
## Im20      NA    NA 0.702     NA     NA    NA    NA     NA    NA    NA    NA
## Im21      NA    NA 0.626     NA     NA    NA    NA     NA    NA    NA    NA
## Im22      NA    NA 0.755     NA     NA    NA    NA     NA    NA    NA    NA
## Im11      NA    NA    NA  0.378     NA    NA    NA     NA    NA    NA    NA
## Im12      NA    NA    NA  0.760     NA    NA    NA     NA    NA    NA    NA
## Im13      NA    NA    NA  0.731     NA    NA    NA     NA    NA    NA    NA
## Im1       NA    NA    NA     NA  0.957    NA    NA     NA    NA    NA    NA
## Im2       NA    NA    NA     NA  0.811    NA    NA     NA    NA    NA    NA
## Im16      NA    NA    NA     NA     NA 0.573    NA     NA    NA    NA    NA
## Im19      NA    NA    NA     NA     NA 0.696    NA     NA    NA    NA    NA
## Im17      NA    NA    NA     NA     NA    NA 0.940     NA    NA    NA    NA
## Im18      NA    NA    NA     NA     NA    NA 0.732     NA    NA    NA    NA
## Im6       NA    NA    NA     NA     NA    NA    NA  0.675    NA    NA    NA
## Im7       NA    NA    NA     NA     NA    NA    NA  0.894    NA    NA    NA
## COM_A1    NA    NA    NA     NA     NA    NA    NA     NA 0.617    NA    NA
## COM_A2    NA    NA    NA     NA     NA    NA    NA     NA 0.689    NA    NA
## COM_A3    NA    NA    NA     NA     NA    NA    NA     NA 0.665    NA    NA
## COM_A4    NA    NA    NA     NA     NA    NA    NA     NA 0.713    NA    NA
## SAT_1     NA    NA    NA     NA     NA    NA    NA     NA    NA 0.738    NA
## SAT_2     NA    NA    NA     NA     NA    NA    NA     NA    NA 0.669    NA
## SAT_3     NA    NA    NA     NA     NA    NA    NA     NA    NA 0.384    NA
## C_REP1    NA    NA    NA     NA     NA    NA    NA     NA    NA    NA 0.636
## C_REP2    NA    NA    NA     NA     NA    NA    NA     NA    NA    NA 0.911
## C_REP3    NA    NA    NA     NA     NA    NA    NA     NA    NA    NA 0.574
## C_CR1     NA    NA    NA     NA     NA    NA    NA     NA    NA    NA    NA
## C_CR3     NA    NA    NA     NA     NA    NA    NA     NA    NA    NA    NA
## C_CR4     NA    NA    NA     NA     NA    NA    NA     NA    NA    NA    NA
##          COI
## Im3       NA
## Im4       NA
## Im5       NA
## Im10      NA
## Im14      NA
## Im20      NA
## Im21      NA
## Im22      NA
## Im11      NA
## Im12      NA
## Im13      NA
## Im1       NA
## Im2       NA
## Im16      NA
## Im19      NA
## Im17      NA
## Im18      NA
## Im6       NA
## Im7       NA
## COM_A1    NA
## COM_A2    NA
## COM_A3    NA
## COM_A4    NA
## SAT_1     NA
## SAT_2     NA
## SAT_3     NA
## C_REP1    NA
## C_REP2    NA
## C_REP3    NA
## C_CR1  0.719
## C_CR3  0.676
## C_CR4  0.648

2.4.3.2.2 Construct reliability criterion

# JONATHAN
# calculate construct reliability (should be above .6)
constrrel <- (t(lambda) %*% ones)^2 / ((t(lambda) %*% ones)^2 + t(theta_lb) %*% ones )
# constrrel

# replace all values satisfying condition with NaN for visibility
constrrel_fail <- constrrel
constrrel_fail[constrrel_fail>.6] <- NaN
constrrel_fail

##          DECO FOOD ATMOS PRODQUAL CHOICE PROF BRAND FRENCH AFCOM SAT  RI COI
## DECO      NaN  NaN   NaN      NaN    NaN  NaN   NaN    NaN   NaN NaN NaN NaN
## FOOD      NaN  NaN   NaN      NaN    NaN  NaN   NaN    NaN   NaN NaN NaN NaN
## ATMOS     NaN  NaN   NaN      NaN    NaN  NaN   NaN    NaN   NaN NaN NaN NaN
## PRODQUAL  NaN  NaN   NaN      NaN    NaN  NaN   NaN    NaN   NaN NaN NaN NaN
## CHOICE    NaN  NaN   NaN      NaN    NaN  NaN   NaN    NaN   NaN NaN NaN NaN
## PROF      NaN  NaN   NaN      NaN    NaN  NaN   NaN    NaN   NaN NaN NaN NaN
## BRAND     NaN  NaN   NaN      NaN    NaN  NaN   NaN    NaN   NaN NaN NaN NaN
## FRENCH    NaN  NaN   NaN      NaN    NaN  NaN   NaN    NaN   NaN NaN NaN NaN
## AFCOM     NaN  NaN   NaN      NaN    NaN  NaN   NaN    NaN   NaN NaN NaN NaN
## SAT       NaN  NaN   NaN      NaN    NaN  NaN   NaN    NaN   NaN NaN NaN NaN
## RI        NaN  NaN   NaN      NaN    NaN  NaN   NaN    NaN   NaN NaN NaN NaN
## COI       NaN  NaN   NaN      NaN    NaN  NaN   NaN    NaN   NaN NaN NaN NaN

# FERESHTEH
#Composite/Construct Reliability
sum.std.loadings<-colSums(std.loadings, na.rm=TRUE)^2
sum.std.theta<-rowSums(std.theta)
sum.std.theta=check*sum.std.theta
CR=sum.std.loadings/(sum.std.loadings+colSums(sum.std.theta))
CR

##      DECO      FOOD     ATMOS  PRODQUAL    CHOICE      PROF     BRAND    FRENCH 
## 0.9215580 0.9360226 0.8718631 0.8289715 0.9382698 0.7758506 0.9103343 0.8787102 
##     AFCOM       SAT        RI       COI 
## 0.8908063 0.8134327 0.8776450 0.8649690

2.4.3.2.3 Average Variance Extracted criterion

# JONATHAN
# calculate Average Variance Extracted (should be above .5)
AVE <- (t(lambda) %*% lambda) / (t(lambda) %*% lambda + t(theta_lb) %*% ones )
# avgvar

# replace all values satisfying condition with NaN for visibility
AVE_fail <- AVE
AVE_fail[AVE_fail>.5] <- NaN
AVE_fail

##          DECO FOOD ATMOS PRODQUAL CHOICE PROF BRAND FRENCH AFCOM SAT  RI COI
## DECO      NaN  NaN   NaN      NaN    NaN  NaN   NaN    NaN   NaN NaN NaN NaN
## FOOD      NaN  NaN   NaN      NaN    NaN  NaN   NaN    NaN   NaN NaN NaN NaN
## ATMOS     NaN  NaN   NaN      NaN    NaN  NaN   NaN    NaN   NaN NaN NaN NaN
## PRODQUAL  NaN  NaN   NaN      NaN    NaN  NaN   NaN    NaN   NaN NaN NaN NaN
## CHOICE    NaN  NaN   NaN      NaN    NaN  NaN   NaN    NaN   NaN NaN NaN NaN
## PROF      NaN  NaN   NaN      NaN    NaN  NaN   NaN    NaN   NaN NaN NaN NaN
## BRAND     NaN  NaN   NaN      NaN    NaN  NaN   NaN    NaN   NaN NaN NaN NaN
## FRENCH    NaN  NaN   NaN      NaN    NaN  NaN   NaN    NaN   NaN NaN NaN NaN
## AFCOM     NaN  NaN   NaN      NaN    NaN  NaN   NaN    NaN   NaN NaN NaN NaN
## SAT       NaN  NaN   NaN      NaN    NaN  NaN   NaN    NaN   NaN NaN NaN NaN
## RI        NaN  NaN   NaN      NaN    NaN  NaN   NaN    NaN   NaN NaN NaN NaN
## COI       NaN  NaN   NaN      NaN    NaN  NaN   NaN    NaN   NaN NaN NaN NaN

# FERESHTEH
#Average Variance Extracted 
std.loadings<- inspect(SEM_fit, what="std")$lambda
std.loadings <- std.loadings^2
AVE_fshteh=colSums(std.loadings)/(colSums(sum.std.theta)+colSums(std.loadings))
AVE_fshteh

##      DECO      FOOD     ATMOS  PRODQUAL    CHOICE      PROF     BRAND    FRENCH 
## 0.7983125 0.8797717 0.6943221 0.6229538 0.8838933 0.6343297 0.8359604 0.7844892 
##     AFCOM       SAT        RI       COI 
## 0.6711567 0.5968399 0.7072306 0.6811421

2.4.3.2.4 Fornell-Larcker Criteria

# JONATHAN
# correlations between constructs (factors...) should be lower than .7
psi = inspect(SEM_fit, what="std")$psi
psi_fail <- psi
psi_fail[psi_fail<.7] <- NaN
psi_fail

##          DECO FOOD ATMOS PRODQU CHOICE PROF BRAND FRENCH AFCOM SAT  RI COI
## DECO        1                                                             
## FOOD      NaN    1                                                        
## ATMOS     NaN  NaN     1                                                  
## PRODQUAL  NaN  NaN   NaN      1                                           
## CHOICE    NaN  NaN   NaN    NaN      1                                    
## PROF      NaN  NaN   NaN    NaN    NaN    1                               
## BRAND     NaN  NaN   NaN    NaN    NaN  NaN     1                         
## FRENCH    NaN  NaN   NaN    NaN    NaN  NaN   NaN      1                  
## AFCOM     NaN  NaN   NaN    NaN    NaN  NaN   NaN    NaN   NaN            
## SAT       NaN  NaN   NaN    NaN    NaN  NaN   NaN    NaN   NaN NaN        
## RI        NaN  NaN   NaN    NaN    NaN  NaN   NaN    NaN   NaN NaN   1    
## COI       NaN  NaN   NaN    NaN    NaN  NaN   NaN    NaN   NaN NaN NaN   1

# JONATHAN
# AVE should be higher than squared correlations between constructs

#psi matrix squared
psi2 <- psi^2

# replace diagonal of psi matrix with AVE values
psi2 <- psi2 - psi2 * diag(1,nrow(psi2),ncol(psi2)) + diag(AVE) * diag(1,nrow(AVE),ncol(AVE))

# create matrix with columns filled with AVE
AVE_full <- AVE
AVE_full[is.na(AVE_full)] <- 0 #replace NAs with 0s
AVE_full <- AVE_full^0 %*% AVE_full # multiply a matrix full of ones with AVE_full to get columns filled with AVE

# substract matrices any psi bigger than AVE will be negative
AVEpsi_fail <- AVE_full - psi2
# AVE_full - psi2
AVEpsi_fail[AVEpsi_fail >= 0] <- NaN

AVE_full

##               DECO      FOOD     ATMOS  PRODQUAL    CHOICE      PROF     BRAND
## DECO     0.7983125 0.8797717 0.6943221 0.6229538 0.8838933 0.6343297 0.8359604
## FOOD     0.7983125 0.8797717 0.6943221 0.6229538 0.8838933 0.6343297 0.8359604
## ATMOS    0.7983125 0.8797717 0.6943221 0.6229538 0.8838933 0.6343297 0.8359604
## PRODQUAL 0.7983125 0.8797717 0.6943221 0.6229538 0.8838933 0.6343297 0.8359604
## CHOICE   0.7983125 0.8797717 0.6943221 0.6229538 0.8838933 0.6343297 0.8359604
## PROF     0.7983125 0.8797717 0.6943221 0.6229538 0.8838933 0.6343297 0.8359604
## BRAND    0.7983125 0.8797717 0.6943221 0.6229538 0.8838933 0.6343297 0.8359604
## FRENCH   0.7983125 0.8797717 0.6943221 0.6229538 0.8838933 0.6343297 0.8359604
## AFCOM    0.7983125 0.8797717 0.6943221 0.6229538 0.8838933 0.6343297 0.8359604
## SAT      0.7983125 0.8797717 0.6943221 0.6229538 0.8838933 0.6343297 0.8359604
## RI       0.7983125 0.8797717 0.6943221 0.6229538 0.8838933 0.6343297 0.8359604
## COI      0.7983125 0.8797717 0.6943221 0.6229538 0.8838933 0.6343297 0.8359604
##             FRENCH     AFCOM       SAT        RI       COI
## DECO     0.7844892 0.6711567 0.5968399 0.7072306 0.6811421
## FOOD     0.7844892 0.6711567 0.5968399 0.7072306 0.6811421
## ATMOS    0.7844892 0.6711567 0.5968399 0.7072306 0.6811421
## PRODQUAL 0.7844892 0.6711567 0.5968399 0.7072306 0.6811421
## CHOICE   0.7844892 0.6711567 0.5968399 0.7072306 0.6811421
## PROF     0.7844892 0.6711567 0.5968399 0.7072306 0.6811421
## BRAND    0.7844892 0.6711567 0.5968399 0.7072306 0.6811421
## FRENCH   0.7844892 0.6711567 0.5968399 0.7072306 0.6811421
## AFCOM    0.7844892 0.6711567 0.5968399 0.7072306 0.6811421
## SAT      0.7844892 0.6711567 0.5968399 0.7072306 0.6811421
## RI       0.7844892 0.6711567 0.5968399 0.7072306 0.6811421
## COI      0.7844892 0.6711567 0.5968399 0.7072306 0.6811421

psi2

##           DECO  FOOD ATMOS PRODQU CHOICE  PROF BRAND FRENCH AFCOM   SAT    RI
## DECO     0.798                                                               
## FOOD     0.173 0.880                                                         
## ATMOS    0.222 0.089 0.694                                                   
## PRODQUAL 0.221 0.204 0.176  0.623                                            
## CHOICE   0.194 0.097 0.210  0.228  0.884                                     
## PROF     0.445 0.275 0.258  0.295  0.373 0.634                               
## BRAND    0.266 0.106 0.270  0.320  0.270 0.379 0.836                         
## FRENCH   0.114 0.345 0.111  0.093  0.053 0.163 0.107  0.784                  
## AFCOM    0.000 0.000 0.000  0.000  0.000 0.000 0.000  0.000 0.671            
## SAT      0.000 0.000 0.000  0.000  0.000 0.000 0.000  0.000 0.127 0.597      
## RI       0.062 0.066 0.145  0.073  0.079 0.139 0.070  0.053 0.000 0.000 0.707
## COI      0.001 0.001 0.045  0.003  0.001 0.003 0.003  0.000 0.000 0.000 0.007
##            COI
## DECO          
## FOOD          
## ATMOS         
## PRODQUAL      
## CHOICE        
## PROF          
## BRAND         
## FRENCH        
## AFCOM         
## SAT           
## RI            
## COI      0.681

AVEpsi_fail

##            DECO   FOOD  ATMOS PRODQU CHOICE   PROF  BRAND FRENCH  AFCOM    SAT
## DECO          .                                                               
## FOOD        NaN      .                                                        
## ATMOS       NaN    NaN      .                                                 
## PRODQUAL    NaN    NaN    NaN      .                                          
## CHOICE      NaN    NaN    NaN    NaN      .                                   
## PROF        NaN    NaN    NaN    NaN    NaN      .                            
## BRAND       NaN    NaN    NaN    NaN    NaN    NaN      .                     
## FRENCH      NaN    NaN    NaN    NaN    NaN    NaN    NaN      .              
## AFCOM       NaN    NaN    NaN    NaN    NaN    NaN    NaN    NaN      .       
## SAT         NaN    NaN    NaN    NaN    NaN    NaN    NaN    NaN    NaN      .
## RI          NaN    NaN    NaN    NaN    NaN    NaN    NaN    NaN    NaN    NaN
## COI         NaN    NaN    NaN    NaN    NaN    NaN    NaN    NaN    NaN    NaN
##              RI    COI
## DECO                  
## FOOD                  
## ATMOS                 
## PRODQUAL              
## CHOICE                
## PROF                  
## BRAND                 
## FRENCH                
## AFCOM                 
## SAT                   
## RI            .       
## COI         NaN      .

# FERESHTEH
std_fit1=inspect(SEM_fit, "std")
std_fit1$psi^2

##           DECO  FOOD ATMOS PRODQU CHOICE  PROF BRAND FRENCH AFCOM   SAT    RI
## DECO     1.000                                                               
## FOOD     0.173 1.000                                                         
## ATMOS    0.222 0.089 1.000                                                   
## PRODQUAL 0.221 0.204 0.176  1.000                                            
## CHOICE   0.194 0.097 0.210  0.228  1.000                                     
## PROF     0.445 0.275 0.258  0.295  0.373 1.000                               
## BRAND    0.266 0.106 0.270  0.320  0.270 0.379 1.000                         
## FRENCH   0.114 0.345 0.111  0.093  0.053 0.163 0.107  1.000                  
## AFCOM    0.000 0.000 0.000  0.000  0.000 0.000 0.000  0.000 0.463            
## SAT      0.000 0.000 0.000  0.000  0.000 0.000 0.000  0.000 0.127 0.335      
## RI       0.062 0.066 0.145  0.073  0.079 0.139 0.070  0.053 0.000 0.000 1.000
## COI      0.001 0.001 0.045  0.003  0.001 0.003 0.003  0.000 0.000 0.000 0.007
##            COI
## DECO          
## FOOD          
## ATMOS         
## PRODQUAL      
## CHOICE        
## PROF          
## BRAND         
## FRENCH        
## AFCOM         
## SAT           
## RI            
## COI      1.000

2.4.3.3 Modification indices

arrange(modificationindices(SEM_fit),-mi)

##          lhs op      rhs     mi    epc sepc.lv sepc.all sepc.nox
## 1      AFCOM =~   C_REP1 61.877  0.158   0.177    0.240    0.240
## 2      ATMOS ~~    AFCOM 49.054 -0.587  -0.507   -0.507   -0.507
## 3      ATMOS  ~    AFCOM 35.588 -0.540  -0.483   -0.483   -0.483
## 4      AFCOM ~~       RI 32.373  0.134   0.247    0.247    0.247
## 5     COM_A1 ~~   COM_A2 31.301  0.288   0.288    0.368    0.368
## 6      AFCOM ~~      COI 31.255  0.406   0.268    0.268    0.268
## 7      ATMOS =~   C_REP1 26.283  0.102   0.127    0.173    0.173
## 8       Im16 ~~     Im19 25.773  0.371   0.371    0.761    0.761
## 9       PROF ~~      SAT 25.773 -0.222  -0.368   -0.368   -0.368
## 10     BRAND =~     Im13 23.807  0.219   0.264    0.219    0.219
## 11    C_REP2 ~~   C_REP3 23.244  0.096   0.096    1.407    1.407
## 12       SAT ~~       RI 22.140  0.089   0.229    0.229    0.229
## 13      Im11 ~~     Im13 21.621 -0.192  -0.192   -0.341   -0.341
## 14       SAT =~   C_REP1 18.223  0.115   0.099    0.135    0.135
## 15        RI =~    SAT_2 17.895  0.232   0.137    0.137    0.137
## 16     BRAND =~     Im12 17.152 -0.178  -0.214   -0.189   -0.189
## 17    CHOICE =~     Im20 16.326 -0.160  -0.208   -0.139   -0.139
## 18        RI =~     Im22 15.906 -0.338  -0.199   -0.130   -0.130
## 19        RI =~   COM_A1 15.392  0.299   0.176    0.123    0.123
## 20      PROF  ~      SAT 14.568 -0.337  -0.322   -0.322   -0.322
## 21    CHOICE =~     Im13 14.137  0.134   0.175    0.145    0.145
## 22      Im11 ~~     Im12 13.137  0.144   0.144    0.286    0.286
## 23    COM_A3 ~~   C_REP1 13.055  0.078   0.078    0.188    0.188
## 24      FOOD =~     Im11 12.685  0.215   0.174    0.152    0.152
## 25     AFCOM =~     Im11 11.893  0.138   0.154    0.135    0.135
## 26    CHOICE =~   C_REP1 11.775  0.059   0.077    0.104    0.104
## 27       SAT  ~   FRENCH 11.592  0.143   0.163    0.163    0.163
## 28  PRODQUAL =~    C_CR4 11.365  0.307   0.216    0.109    0.109
## 29      PROF =~   COM_A3 11.354  0.198   0.180    0.112    0.112
## 30      Im21 ~~   C_REP3 11.319  0.052   0.052    0.171    0.171
## 31     ATMOS =~     Im12 11.112 -0.116  -0.146   -0.128   -0.128
## 32     AFCOM =~     Im20 10.705 -0.168  -0.188   -0.126   -0.126
## 33    FRENCH =~   C_REP1 10.658  0.075   0.074    0.100    0.100
## 34    CHOICE =~     Im12 10.534 -0.111  -0.144   -0.127   -0.127
## 35      Im21 ~~     Im22 10.334 -0.190  -0.190   -0.299   -0.299
## 36      Im13 ~~      Im1 10.251  0.066   0.066    0.382    0.382
## 37  PRODQUAL ~~    AFCOM  9.881 -0.142  -0.219   -0.219   -0.219
## 38      DECO =~   C_REP1  9.764  0.056   0.069    0.094    0.094
## 39     AFCOM  ~   CHOICE  9.453  0.130   0.151    0.151    0.151
## 40       SAT =~   COM_A2  9.449 -0.194  -0.168   -0.106   -0.106
## 41      Im13 ~~     Im17  9.292  0.068   0.068    0.358    0.358
## 42       SAT =~   COM_A3  9.262  0.199   0.173    0.107    0.107
## 43     AFCOM  ~      SAT  9.120  0.359   0.278    0.278    0.278
## 44       Im4 ~~     Im17  9.042 -0.045  -0.045   -0.453   -0.453
## 45       Im1 ~~    SAT_2  9.041 -0.055  -0.055   -0.346   -0.346
## 46  PRODQUAL  ~    AFCOM  8.849 -0.148  -0.235   -0.235   -0.235
## 47       SAT  ~    AFCOM  8.555  0.220   0.284    0.284    0.284
## 48      Im20 ~~     Im22  8.506  0.205   0.205    0.333    0.333
## 49      Im10 ~~     Im16  8.198  0.046   0.046    0.173    0.173
## 50       SAT =~     Im12  8.068 -0.129  -0.112   -0.099   -0.099
## 51     ATMOS =~     Im11  7.837  0.111   0.138    0.121    0.121
## 52     AFCOM =~     Im12  7.657 -0.091  -0.102   -0.090   -0.090
## 53      Im14 ~~     Im16  7.416 -0.043  -0.043   -0.212   -0.212
## 54      Im20 ~~     Im21  7.388  0.150   0.150    0.219    0.219
## 55  PRODQUAL =~    C_CR1  7.333 -0.237  -0.166   -0.086   -0.086
## 56    FRENCH =~     Im22  7.319  0.137   0.135    0.088    0.088
## 57       COI =~   C_REP1  7.224  0.036   0.060    0.081    0.081
## 58     ATMOS =~    C_CR4  7.213  0.140   0.176    0.089    0.089
## 59      Im10 ~~   COM_A2  7.207  0.049   0.049    0.162    0.162
## 60      DECO =~   COM_A3  7.153  0.107   0.132    0.082    0.082
## 61     BRAND =~     Im20  7.150 -0.123  -0.148   -0.099   -0.099
## 62      FOOD =~   C_REP1  7.149  0.074   0.060    0.081    0.081
## 63    CHOICE =~   C_REP3  7.114 -0.037  -0.048   -0.086   -0.086
## 64       SAT =~    C_CR4  7.053  0.194   0.169    0.086    0.086
## 65    COM_A1 ~~   COM_A4  7.039 -0.148  -0.148   -0.183   -0.183
## 66    FRENCH =~   C_REP2  7.027 -0.050  -0.050   -0.079   -0.079
## 67     ATMOS =~   C_REP3  6.995 -0.042  -0.053   -0.094   -0.094
## 68     AFCOM  ~     PROF  6.907  0.199   0.162    0.162    0.162
## 69     BRAND =~     Im22  6.898  0.122   0.148    0.097    0.097
## 70       SAT ~~      COI  6.822 -0.152  -0.140   -0.140   -0.140
## 71      Im19 ~~   C_REP1  6.618 -0.040  -0.040   -0.145   -0.145
## 72        RI =~     Im16  6.453 -0.207  -0.122   -0.101   -0.101
## 73      Im10 ~~      Im6  6.414 -0.036  -0.036   -0.152   -0.152
## 74    FRENCH =~     Im16  6.315 -0.127  -0.126   -0.104   -0.104
## 75    CHOICE =~      Im5  6.298  0.086   0.112    0.085    0.085
## 76     BRAND =~      Im4  6.287 -0.067  -0.081   -0.060   -0.060
## 77      PROF =~     Im12  6.238 -0.152  -0.138   -0.122   -0.122
## 78  PRODQUAL =~      Im5  6.228  0.173   0.121    0.091    0.091
## 79     BRAND =~    C_CR4  6.197  0.127   0.153    0.078    0.078
## 80      PROF =~   C_REP1  6.135  0.069   0.062    0.085    0.085
## 81      Im22 ~~      Im1  6.117  0.062   0.062    0.296    0.296
## 82     ATMOS =~      Im5  6.069  0.095   0.119    0.089    0.089
## 83    C_REP1 ~~   C_REP2  6.068 -0.076  -0.076   -0.909   -0.909
## 84     SAT_2 ~~    SAT_3  6.011 -0.090  -0.090   -0.177   -0.177
## 85      DECO =~    C_CR4  5.821  0.119   0.147    0.075    0.075
## 86     BRAND =~      Im5  5.807  0.096   0.115    0.087    0.087
## 87      FOOD =~      Im6  5.787 -0.269  -0.218   -0.182   -0.182
## 88     BRAND =~   COM_A3  5.704  0.099   0.120    0.074    0.074
## 89      PROF =~    C_CR4  5.642  0.168   0.153    0.078    0.078
## 90      Im13 ~~     Im16  5.612 -0.070  -0.070   -0.144   -0.144
## 91      DECO =~     Im18  5.593  0.101   0.125    0.089    0.089
## 92      DECO =~     Im17  5.593 -0.102  -0.126   -0.101   -0.101
## 93     SAT_1 ~~    SAT_3  5.570  0.092   0.092    0.200    0.200
## 94    COM_A3 ~~   COM_A4  5.532  0.152   0.152    0.176    0.176
## 95       Im3 ~~      Im1  5.490 -0.034  -0.034   -0.265   -0.265
## 96      Im10 ~~      Im7  5.466  0.034   0.034    0.252    0.252
## 97    COM_A1 ~~   C_REP2  5.455  0.034   0.034    0.207    0.207
## 98      Im22 ~~     Im12  5.408 -0.068  -0.068   -0.163   -0.163
## 99      Im11 ~~      Im6  5.400 -0.072  -0.072   -0.116   -0.116
## 100    AFCOM =~    C_CR4  5.370  0.129   0.144    0.073    0.073
## 101     Im22 ~~   C_REP2  5.355 -0.033  -0.033   -0.234   -0.234
## 102     Im16 ~~    SAT_1  5.322 -0.061  -0.061   -0.150   -0.150
## 103    ATMOS =~   C_REP2  5.286 -0.039  -0.049   -0.077   -0.077
## 104     FOOD =~   COM_A3  5.281  0.140   0.113    0.070    0.070
## 105      Im1 ~~    SAT_1  5.167  0.041   0.041    0.287    0.287
## 106     DECO =~     Im20  5.076 -0.095  -0.117   -0.079   -0.079
## 107     DECO =~   C_REP3  5.036 -0.032  -0.040   -0.072   -0.072
## 108     FOOD =~     Im13  5.010 -0.125  -0.102   -0.084   -0.084
## 109      Im5 ~~      Im6  5.010 -0.066  -0.066   -0.112   -0.112
## 110     DECO =~    C_CR1  5.008 -0.106  -0.131   -0.068   -0.068
## 111     DECO =~      Im7  4.885 -0.084  -0.104   -0.086   -0.086
## 112     PROF =~   COM_A2  4.882 -0.125  -0.114   -0.071   -0.071
## 113   CHOICE ~~    AFCOM  4.865  0.101   0.084    0.084    0.084
## 114   C_REP1 ~~   C_REP3  4.856 -0.036  -0.036   -0.225   -0.225
## 115      Im4 ~~    C_CR1  4.822 -0.064  -0.064   -0.191   -0.191
## 116      Im4 ~~     Im18  4.818  0.040   0.040    0.168    0.168
## 117     Im10 ~~     Im13  4.805 -0.031  -0.031   -0.145   -0.145
## 118     FOOD =~   C_REP2  4.798 -0.051  -0.041   -0.065   -0.065
## 119     Im13 ~~      Im2  4.787 -0.045  -0.045   -0.129   -0.129
## 120      Im3 ~~     Im22  4.764  0.049   0.049    0.139    0.139
## 121   FRENCH =~     Im20  4.724 -0.109  -0.107   -0.072   -0.072
## 122     FOOD =~      Im5  4.677  0.120   0.097    0.073    0.073
## 123     FOOD =~      Im7  4.663  0.284   0.230    0.190    0.190
## 124     Im22 ~~   C_REP3  4.654 -0.034  -0.034   -0.123   -0.123
## 125     Im20 ~~     Im17  4.627 -0.058  -0.058   -0.233   -0.233
## 126     PROF =~    SAT_2  4.584  0.130   0.118    0.119    0.119
## 127     Im22 ~~    SAT_1  4.558  0.058   0.058    0.148    0.148
## 128     PROF =~   C_REP3  4.558 -0.048  -0.043   -0.078   -0.078
## 129      Im4 ~~   COM_A3  4.540  0.051   0.051    0.168    0.168
## 130    BRAND =~    C_CR1  4.516 -0.104  -0.126   -0.065   -0.065
## 131   CHOICE  ~    AFCOM  4.498  0.114   0.098    0.098    0.098
## 132     Im11 ~~   C_REP1  4.467  0.041   0.041    0.102    0.102
## 133   COM_A1 ~~    SAT_1  4.359 -0.059  -0.059   -0.128   -0.128
## 134      COI =~   COM_A4  4.335  0.063   0.104    0.060    0.060
## 135      Im3 ~~      Im4  4.333  0.148   0.148    0.977    0.977
## 136       RI =~     Im12  4.281 -0.133  -0.078   -0.069   -0.069
## 137      Im3 ~~      Im5  4.266 -0.068  -0.068   -0.169   -0.169
## 138   FRENCH ~~      SAT  4.214  0.060   0.093    0.093    0.093
## 139      COI =~    SAT_1  4.213 -0.039  -0.064   -0.063   -0.063
## 140    BRAND =~      Im7  4.204 -0.079  -0.096   -0.079   -0.079
## 141    AFCOM =~      Im5  4.180  0.079   0.088    0.066    0.066
## 142     DECO =~      Im6  4.175  0.067   0.083    0.069    0.069
## 143       RI =~     Im21  4.151  0.163   0.096    0.070    0.070
## 144    ATMOS =~      Im4  4.122 -0.052  -0.065   -0.048   -0.048
## 145     Im14 ~~   COM_A2  4.095 -0.036  -0.036   -0.156   -0.156
## 146 PRODQUAL =~      Im2  4.068 -0.124  -0.087   -0.068   -0.068
## 147     DECO =~   COM_A2  4.009 -0.077  -0.095   -0.059   -0.059
## 148     Im20 ~~      Im6  3.960 -0.062  -0.062   -0.111   -0.111
## 149   CHOICE =~   COM_A3  3.948  0.074   0.097    0.060    0.060
## 150     PROF =~     Im13  3.914  0.126   0.114    0.095    0.095
## 151      SAT =~    C_CR1  3.891 -0.138  -0.120   -0.062   -0.062
## 152     PROF =~     Im20  3.844 -0.126  -0.115   -0.077   -0.077
## 153    BRAND =~   C_REP3  3.843 -0.029  -0.036   -0.064   -0.064
## 154     Im16 ~~   C_REP3  3.839 -0.029  -0.029   -0.102   -0.102
## 155    BRAND =~      Im6  3.805  0.065   0.079    0.066    0.066
## 156 PRODQUAL =~      Im1  3.759  0.134   0.094    0.071    0.071
## 157      Im7 ~~   C_REP2  3.754 -0.022  -0.022   -0.298   -0.298
## 158     DECO =~     Im22  3.749  0.083   0.102    0.067    0.067
## 159   COM_A4 ~~    C_CR4  3.747  0.121   0.121    0.112    0.112
## 160     FOOD =~    C_CR4  3.740  0.147   0.119    0.060    0.060
## 161      SAT  ~    ATMOS  3.739  0.072   0.104    0.104    0.104
## 162    SAT_3 ~~    C_CR3  3.717 -0.111  -0.111   -0.106   -0.106
## 163      COI =~     Im19  3.711  0.050   0.083    0.073    0.073
## 164   COM_A2 ~~    SAT_2  3.687 -0.057  -0.057   -0.113   -0.113
## 165     Im20 ~~   COM_A4  3.684  0.085   0.085    0.113    0.113
## 166     Im20 ~~     Im13  3.683  0.061   0.061    0.120    0.120
## 167      Im4 ~~      Im6  3.674  0.033   0.033    0.148    0.148
## 168     Im11 ~~      Im1  3.661 -0.047  -0.047   -0.190   -0.190
## 169     Im22 ~~    SAT_2  3.643 -0.053  -0.053   -0.121   -0.121
## 170       RI =~      Im5  3.628  0.136   0.080    0.060    0.060
## 171   COM_A1 ~~   COM_A3  3.553 -0.099  -0.099   -0.120   -0.120
## 172   COM_A2 ~~   COM_A3  3.545 -0.111  -0.111   -0.134   -0.134
## 173    SAT_1 ~~    C_CR1  3.534 -0.069  -0.069   -0.130   -0.130
## 174      Im3 ~~   COM_A4  3.528  0.048   0.048    0.112    0.112
## 175     Im22 ~~     Im11  3.500  0.071   0.071    0.105    0.105
## 176     PROF =~    C_CR1  3.432 -0.126  -0.115   -0.059   -0.059
## 177      Im2 ~~     Im17  3.429  0.032   0.032    0.188    0.188
## 178    ATMOS =~   COM_A4  3.391  0.094   0.118    0.069    0.069
## 179      Im3 ~~     Im17  3.378  0.028   0.028    0.201    0.201
## 180     Im13 ~~   C_REP2  3.372  0.022   0.022    0.185    0.185
## 181     Im22 ~~   C_REP1  3.355  0.035   0.035    0.105    0.105
## 182     PROF =~      Im2  3.355  0.161   0.147    0.114    0.114
## 183     PROF =~      Im1  3.354 -0.181  -0.165   -0.124   -0.124
## 184   C_REP2 ~~    C_CR4  3.348 -0.037  -0.037   -0.171   -0.171
## 185   FRENCH  ~      SAT  3.327  0.124   0.109    0.109    0.109
## 186     Im13 ~~   C_REP1  3.251 -0.029  -0.029   -0.103   -0.103
## 187     Im20 ~~    SAT_2  3.249  0.050   0.050    0.108    0.108
## 188     Im14 ~~      Im6  3.218  0.025   0.025    0.142    0.142
## 189      COI =~   C_REP2  3.212 -0.020  -0.033   -0.052   -0.052
## 190     Im22 ~~   COM_A1  3.204 -0.071  -0.071   -0.106   -0.106
## 191    AFCOM =~   C_REP3  3.175 -0.029  -0.033   -0.058   -0.058
## 192      COI =~     Im11  3.174  0.048   0.078    0.069    0.069
## 193     PROF =~    SAT_1  3.159 -0.113  -0.103   -0.102   -0.102
## 194      Im1 ~~   C_REP3  3.154 -0.018  -0.018   -0.179   -0.179
## 195     Im11 ~~     Im17  3.129 -0.047  -0.047   -0.169   -0.169
## 196   COM_A2 ~~    C_CR1  3.120  0.099   0.099    0.108    0.108
## 197     Im20 ~~   COM_A2  3.119 -0.074  -0.074   -0.102   -0.102
## 198     Im18 ~~      Im6  3.098  0.046   0.046    0.092    0.092
## 199     Im17 ~~   C_REP1  3.076 -0.023  -0.023   -0.172   -0.172
## 200      Im5 ~~   C_REP1  3.034  0.032   0.032    0.084    0.084
## 201   FRENCH =~     Im11  3.032  0.081   0.080    0.070    0.070
## 202 PRODQUAL =~     Im16  3.000 -0.148  -0.104   -0.087   -0.087
## 203     Im14 ~~    SAT_2  2.981  0.021   0.021    0.139    0.139
## 204 PRODQUAL =~   C_REP3  2.970 -0.046  -0.033   -0.059   -0.059
## 205     Im18 ~~   COM_A1  2.961 -0.057  -0.057   -0.090   -0.090
## 206      Im3 ~~      Im2  2.955  0.025   0.025    0.097    0.097
## 207    BRAND =~   C_REP1  2.929  0.032   0.038    0.052    0.052
## 208   COM_A1 ~~    C_CR3  2.928  0.099   0.099    0.096    0.096
## 209     Im13 ~~   COM_A2  2.909 -0.058  -0.058   -0.104   -0.104
## 210     Im14 ~~      Im7  2.900 -0.025  -0.025   -0.243   -0.243
## 211   COM_A4 ~~    SAT_1  2.891  0.053   0.053    0.111    0.111
## 212   FRENCH =~    C_CR4  2.880  0.108   0.106    0.054    0.054
## 213      Im5 ~~      Im1  2.857  0.040   0.040    0.168    0.168
## 214   FRENCH =~   COM_A3  2.841  0.090   0.089    0.055    0.055
## 215    ATMOS =~   COM_A1  2.817 -0.076  -0.095   -0.067   -0.067
## 216     Im10 ~~     Im11  2.794  0.028   0.028    0.092    0.092
## 217     Im22 ~~      Im2  2.792 -0.042  -0.042   -0.099   -0.099
## 218      SAT =~     Im19  2.751 -0.121  -0.105   -0.093   -0.093
## 219     Im10 ~~    C_CR1  2.731  0.038   0.038    0.109    0.109
## 220     Im14 ~~    C_CR1  2.727 -0.037  -0.037   -0.140   -0.140
## 221    SAT_2 ~~   C_REP1  2.724  0.023   0.023    0.090    0.090
## 222      Im5 ~~     Im14  2.721  0.026   0.026    0.117    0.117
## 223      Im2 ~~    C_CR1  2.710  0.056   0.056    0.098    0.098
## 224       RI =~     Im11  2.694  0.124   0.073    0.064    0.064
## 225      Im5 ~~      Im7  2.692  0.047   0.047    0.137    0.137
## 226   COM_A1 ~~    SAT_3  2.689  0.066   0.066    0.084    0.084
## 227      SAT =~      Im5  2.676  0.086   0.074    0.056    0.056
## 228     Im21 ~~    C_CR3  2.672 -0.091  -0.091   -0.092   -0.092
## 229      Im2 ~~    SAT_2  2.671  0.030   0.030    0.093    0.093
## 230      Im1 ~~     Im17  2.669 -0.029  -0.029   -0.347   -0.347
## 231     Im12 ~~      Im7  2.643  0.038   0.038    0.172    0.172
## 232      SAT =~     Im20  2.596 -0.092  -0.080   -0.053   -0.053
## 233     Im19 ~~    SAT_1  2.588 -0.038  -0.038   -0.117   -0.117
## 234      Im2 ~~     Im16  2.587  0.038   0.038    0.087    0.087
## 235   COM_A2 ~~    SAT_1  2.580 -0.047  -0.047   -0.103   -0.103
## 236     Im20 ~~   COM_A1  2.563 -0.064  -0.064   -0.089   -0.089
## 237   CHOICE =~     Im22  2.551  0.064   0.083    0.054    0.054
## 238    ATMOS =~    C_CR1  2.545 -0.080  -0.100   -0.052   -0.052
## 239    ATMOS =~     Im13  2.531  0.058   0.073    0.061    0.061
## 240   C_REP3 ~~    C_CR3  2.505 -0.037  -0.037   -0.086   -0.086
## 241     Im14 ~~   C_REP3  2.490  0.011   0.011    0.114    0.114
## 242    AFCOM =~    SAT_2  2.425  0.053   0.060    0.060    0.060
## 243      Im2 ~~   C_REP1  2.403  0.020   0.020    0.079    0.079
## 244      Im4 ~~     Im11  2.402 -0.033  -0.033   -0.112   -0.112
## 245      Im3 ~~    C_CR1  2.396  0.047   0.047    0.099    0.099
## 246      Im4 ~~     Im22  2.381 -0.033  -0.033   -0.134   -0.134
## 247   COM_A4 ~~    SAT_3  2.375 -0.069  -0.069   -0.083   -0.083
## 248   CHOICE =~     Im14  2.365  0.026   0.034    0.039    0.039
## 249   CHOICE =~     Im10  2.364 -0.025  -0.033   -0.038   -0.038
## 250      Im5 ~~   COM_A2  2.363  0.061   0.061    0.079    0.079
## 251     FOOD =~    C_CR1  2.363 -0.112  -0.091   -0.047   -0.047
## 252     Im22 ~~    SAT_3  2.338 -0.060  -0.060   -0.088   -0.088
## 253     Im11 ~~   C_REP2  2.334 -0.022  -0.022   -0.128   -0.128
## 254      SAT =~     Im11  2.319  0.084   0.073    0.064    0.064
## 255     FOOD =~    SAT_2  2.311  0.063   0.051    0.052    0.052
## 256     Im20 ~~      Im1  2.293 -0.038  -0.038   -0.169   -0.169
## 257   COM_A4 ~~   C_REP1  2.283  0.033   0.033    0.081    0.081
## 258 PRODQUAL =~    SAT_2  2.262  0.078   0.055    0.055    0.055
## 259   COM_A3 ~~   C_REP2  2.256 -0.024  -0.024   -0.136   -0.136
## 260   COM_A2 ~~   COM_A4  2.244 -0.096  -0.096   -0.118   -0.118
## 261      SAT =~     Im16  2.223 -0.113  -0.098   -0.081   -0.081
## 262   FRENCH =~      Im1  2.216 -0.051  -0.050   -0.038   -0.038
## 263     FOOD =~     Im16  2.214 -0.100  -0.081   -0.067   -0.067
## 264     Im21 ~~     Im18  2.214 -0.047  -0.047   -0.078   -0.078
## 265     Im13 ~~   COM_A3  2.212 -0.052  -0.052   -0.090   -0.090
## 266      SAT =~     Im13  2.196  0.072   0.062    0.052    0.052
## 267      Im2 ~~   C_REP2  2.177 -0.014  -0.014   -0.131   -0.131
## 268     Im22 ~~      Im7  2.176  0.044   0.044    0.149    0.149
## 269     Im19 ~~   COM_A1  2.173  0.047   0.047    0.086    0.086
## 270    AFCOM =~      Im2  2.170  0.041   0.045    0.035    0.035
## 271   COM_A3 ~~   C_REP3  2.156 -0.026  -0.026   -0.076   -0.076
## 272     DECO =~     Im12  2.149 -0.052  -0.065   -0.057   -0.057
## 273      Im5 ~~     Im16  2.143 -0.051  -0.051   -0.074   -0.074
## 274     Im13 ~~    SAT_2  2.137  0.033   0.033    0.092    0.092
## 275   FRENCH =~    SAT_1  2.131  0.048   0.048    0.047    0.047
## 276      Im3 ~~     Im20  2.127 -0.033  -0.033   -0.087   -0.087
## 277      COI =~      Im2  2.123  0.025   0.042    0.032    0.032
## 278      Im4 ~~      Im1  2.121  0.020   0.020    0.226    0.226
## 279      COI =~     Im13  2.103 -0.034  -0.056   -0.046   -0.046
## 280      COI =~   COM_A2  2.066  0.041   0.068    0.043    0.043
## 281      Im3 ~~   COM_A3  2.063 -0.036  -0.036   -0.084   -0.084
## 282    BRAND =~    SAT_2  2.060  0.043   0.052    0.052    0.052
## 283 PRODQUAL =~      Im6  2.054 -0.086  -0.060   -0.050   -0.050
## 284 PRODQUAL =~      Im7  2.054  0.100   0.070    0.058    0.058
## 285     Im22 ~~     Im19  2.047 -0.045  -0.045   -0.095   -0.095
## 286     Im10 ~~     Im17  2.044 -0.017  -0.017   -0.162   -0.162
## 287     Im16 ~~    C_CR4  2.028 -0.074  -0.074   -0.080   -0.080
## 288     Im22 ~~     Im18  2.023  0.046   0.046    0.084    0.084
## 289   FRENCH =~   COM_A2  2.019 -0.073  -0.072   -0.045   -0.045
## 290      Im3 ~~     Im12  2.015 -0.024  -0.024   -0.094   -0.094
## 291     Im12 ~~     Im16  2.003  0.039   0.039    0.090    0.090
## 292      Im2 ~~    SAT_1  1.991 -0.025  -0.025   -0.087   -0.087
## 293     Im12 ~~    SAT_3  1.984  0.042   0.042    0.085    0.085
## 294     Im18 ~~   C_REP1  1.983  0.023   0.023    0.071    0.071
## 295     Im19 ~~   C_REP2  1.960  0.017   0.017    0.143    0.143
## 296     Im21 ~~    C_CR4  1.960  0.076   0.076    0.077    0.077
## 297     Im14 ~~     Im17  1.948  0.016   0.016    0.206    0.206
## 298      Im2 ~~   COM_A3  1.923  0.039   0.039    0.075    0.075
## 299      SAT =~     Im18  1.917 -0.073  -0.064   -0.046   -0.046
## 300     Im14 ~~   COM_A3  1.909  0.026   0.026    0.106    0.106
## 301     Im14 ~~      Im2  1.900  0.015   0.015    0.103    0.103
## 302     FOOD =~      Im1  1.888 -0.060  -0.049   -0.037   -0.037
## 303     Im12 ~~    SAT_1  1.877 -0.028  -0.028   -0.098   -0.098
## 304    C_CR1 ~~    C_CR3  1.851  0.543   0.543    0.451    0.451
## 305     Im10 ~~   COM_A4  1.834 -0.026  -0.026   -0.083   -0.083
## 306      Im7 ~~   COM_A1  1.820 -0.041  -0.041   -0.119   -0.119
## 307     Im11 ~~      Im7  1.810  0.040   0.040    0.112    0.112
## 308     Im11 ~~   COM_A3  1.799  0.058   0.058    0.068    0.068
## 309   COM_A3 ~~    SAT_2  1.794  0.042   0.042    0.078    0.078
## 310      SAT =~      Im2  1.787  0.065   0.056    0.044    0.044
## 311    BRAND =~      Im3  1.782  0.035   0.042    0.032    0.032
## 312     Im20 ~~    SAT_1  1.779 -0.036  -0.036   -0.086   -0.086
## 313   COM_A2 ~~    SAT_3  1.771  0.056   0.056    0.071    0.071
## 314   COM_A1 ~~   C_REP3  1.769  0.022   0.022    0.067    0.067
## 315   CHOICE =~    SAT_2  1.768 -0.041  -0.054   -0.054   -0.054
## 316   CHOICE =~    C_CR4  1.742  0.062   0.080    0.041    0.041
## 317    ATMOS =~    SAT_2  1.740  0.037   0.047    0.047    0.047
## 318     PROF =~      Im4  1.737 -0.065  -0.059   -0.044   -0.044
## 319     Im10 ~~    SAT_2  1.735 -0.016  -0.016   -0.083   -0.083
## 320   FRENCH =~      Im5  1.729  0.059   0.058    0.043    0.043
## 321     Im19 ~~     Im17  1.718  0.030   0.030    0.158    0.158
## 322   FRENCH =~    C_CR1  1.715 -0.080  -0.079   -0.041   -0.041
## 323     Im20 ~~   COM_A3  1.713 -0.057  -0.057   -0.075   -0.075
## 324      Im7 ~~   COM_A2  1.692 -0.042  -0.042   -0.119   -0.119
## 325      COI =~      Im1  1.689 -0.025  -0.042   -0.031   -0.031
## 326     Im12 ~~      Im6  1.663 -0.030  -0.030   -0.080   -0.080
## 327       RI =~     Im14  1.662  0.047   0.028    0.032    0.032
## 328       RI =~     Im10  1.662 -0.046  -0.027   -0.031   -0.031
## 329     Im13 ~~   COM_A4  1.659  0.046   0.046    0.080    0.080
## 330       RI =~      Im7  1.647 -0.094  -0.055   -0.046   -0.046
## 331     Im11 ~~      Im2  1.627  0.032   0.032    0.063    0.063
## 332      COI =~     Im22  1.622 -0.037  -0.061   -0.040   -0.040
## 333      Im3 ~~     Im14  1.617 -0.012  -0.012   -0.103   -0.103
## 334   C_REP1 ~~    C_CR3  1.612  0.036   0.036    0.069    0.069
## 335      Im5 ~~    SAT_2  1.610  0.034   0.034    0.068    0.068
## 336 PRODQUAL =~      Im4  1.608 -0.058  -0.041   -0.030   -0.030
## 337       RI =~     Im19  1.585 -0.099  -0.058   -0.052   -0.052
## 338     Im12 ~~    C_CR4  1.580  0.053   0.053    0.081    0.081
## 339      COI =~      Im4  1.558 -0.020  -0.032   -0.024   -0.024
## 340      SAT =~     Im17  1.554  0.057   0.049    0.040    0.040
## 341      Im7 ~~    SAT_3  1.540  0.038   0.038    0.107    0.107
## 342     Im12 ~~     Im17  1.539 -0.026  -0.026   -0.154   -0.154
## 343     Im17 ~~   COM_A1  1.518  0.033   0.033    0.124    0.124
## 344   FRENCH =~      Im2  1.509  0.038   0.037    0.029    0.029
## 345      Im1 ~~   COM_A4  1.504 -0.034  -0.034   -0.135   -0.135
## 346     Im10 ~~     Im18  1.499  0.018   0.018    0.071    0.071
## 347      Im4 ~~      Im2  1.495 -0.017  -0.017   -0.094   -0.094
## 348       RI =~     Im13  1.495  0.082   0.048    0.040    0.040
## 349   CHOICE =~     Im21  1.486  0.046   0.060    0.043    0.043
## 350      Im2 ~~     Im18  1.484 -0.026  -0.026   -0.063   -0.063
## 351   CHOICE  ~      SAT  1.479  0.210   0.140    0.140    0.140
## 352   C_REP3 ~~    C_CR4  1.479  0.027   0.027    0.064    0.064
## 353     Im11 ~~    SAT_1  1.457  0.033   0.033    0.070    0.070
## 354     PROF =~      Im5  1.424  0.081   0.074    0.055    0.055
## 355     DECO =~     Im13  1.423  0.045   0.055    0.046    0.046
## 356     Im12 ~~     Im13  1.421  0.088   0.088    0.252    0.252
## 357     Im18 ~~   COM_A2  1.416  0.041   0.041    0.064    0.064
## 358   COM_A1 ~~    SAT_2  1.415  0.034   0.034    0.067    0.067
## 359     FOOD =~      Im2  1.413  0.046   0.038    0.029    0.029
## 360     Im12 ~~   C_REP1  1.409 -0.018  -0.018   -0.071   -0.071
## 361    AFCOM  ~     DECO  1.398  0.054   0.059    0.059    0.059
## 362     DECO ~~      SAT  1.396 -0.146  -0.179   -0.179   -0.179
## 363     Im14 ~~     Im18  1.395 -0.016  -0.016   -0.088   -0.088
## 364     Im21 ~~    SAT_3  1.392  0.045   0.045    0.061    0.061
## 365      SAT =~   COM_A1  1.385  0.070   0.061    0.043    0.043
## 366      Im1 ~~   COM_A1  1.385  0.030   0.030    0.123    0.123
## 367     Im18 ~~      Im7  1.381 -0.029  -0.029   -0.103   -0.103
## 368   COM_A3 ~~    C_CR3  1.376  0.074   0.074    0.068    0.068
## 369    SAT_2 ~~    C_CR3  1.376  0.048   0.048    0.071    0.071
## 370     Im14 ~~    C_CR4  1.375  0.028   0.028    0.092    0.092
## 371     Im10 ~~     Im12  1.375  0.015   0.015    0.081    0.081
## 372      SAT =~      Im4  1.372 -0.039  -0.034   -0.025   -0.025
## 373    AFCOM =~     Im16  1.367 -0.047  -0.053   -0.044   -0.044
## 374      Im3 ~~     Im18  1.357 -0.022  -0.022   -0.066   -0.066
## 375     Im19 ~~     Im18  1.354 -0.031  -0.031   -0.068   -0.068
## 376     Im18 ~~   C_REP3  1.351 -0.015  -0.015   -0.058   -0.058
## 377    ATMOS =~     Im17  1.348 -0.052  -0.065   -0.053   -0.053
## 378    ATMOS =~     Im18  1.348  0.052   0.065    0.046    0.046
## 379      Im4 ~~     Im12  1.347  0.019   0.019    0.105    0.105
## 380   CHOICE =~   COM_A1  1.346  0.040   0.052    0.036    0.036
## 381      Im5 ~~     Im19  1.341 -0.034  -0.034   -0.064   -0.064
## 382     Im13 ~~    SAT_3  1.338 -0.037  -0.037   -0.066   -0.066
## 383      Im3 ~~     Im11  1.307  0.026   0.026    0.061    0.061
## 384    SAT_1 ~~    C_CR4  1.304  0.044   0.044    0.073    0.073
## 385    ATMOS =~   COM_A2  1.298 -0.055  -0.069   -0.043   -0.043
## 386     Im20 ~~   C_REP2  1.295  0.016   0.016    0.108    0.108
## 387    BRAND =~     Im16  1.284 -0.059  -0.071   -0.059   -0.059
## 388    SAT_1 ~~   C_REP3  1.284  0.013   0.013    0.067    0.067
## 389      Im6 ~~      Im7  1.281  0.435   0.435    1.612    1.612
## 390   FRENCH ~~    AFCOM  1.280 -0.077  -0.085   -0.085   -0.085
## 391       RI =~   COM_A3  1.276  0.094   0.055    0.034    0.034
## 392 PRODQUAL =~     Im17  1.271  0.103   0.072    0.058    0.058
## 393 PRODQUAL =~     Im18  1.271 -0.102  -0.072   -0.051   -0.051
## 394     Im14 ~~     Im21  1.262  0.018   0.018    0.084    0.084
## 395     Im22 ~~    C_CR1  1.256 -0.058  -0.058   -0.075   -0.075
## 396     Im12 ~~   COM_A4  1.239 -0.037  -0.037   -0.072   -0.072
## 397       RI =~   COM_A4  1.230  0.093   0.055    0.032    0.032
## 398     Im20 ~~   C_REP3  1.225 -0.018  -0.018   -0.059   -0.059
## 399      Im3 ~~     Im10  1.223  0.011   0.011    0.070    0.070
## 400 PRODQUAL =~   COM_A2  1.213 -0.078  -0.055   -0.035   -0.035
## 401   FRENCH =~    SAT_3  1.209  0.051   0.050    0.044    0.044
## 402     Im10 ~~    C_CR4  1.207 -0.027  -0.027   -0.067   -0.067
## 403      Im4 ~~   COM_A4  1.202 -0.027  -0.027   -0.089   -0.089
## 404 PRODQUAL =~     Im20  1.186  0.083   0.058    0.039    0.039
## 405     PROF ~~    AFCOM  1.182  0.034   0.040    0.040    0.040
## 406   CHOICE =~    SAT_1  1.178  0.035   0.046    0.045    0.045
## 407      COI =~     Im20  1.152 -0.031  -0.051   -0.034   -0.034
## 408 PRODQUAL =~     Im22  1.149 -0.083  -0.058   -0.038   -0.038
## 409     Im10 ~~   C_REP3  1.147 -0.007  -0.007   -0.060   -0.060
## 410    SAT_1 ~~    C_CR3  1.144 -0.042  -0.042   -0.070   -0.070
## 411      COI =~    SAT_2  1.136  0.020   0.034    0.034    0.034
## 412     Im16 ~~      Im7  1.135 -0.030  -0.030   -0.098   -0.098
## 413 PRODQUAL =~     Im19  1.134  0.088   0.062    0.055    0.055
## 414      Im1 ~~   COM_A3  1.105 -0.029  -0.029   -0.113   -0.113
## 415     Im16 ~~    C_CR1  1.098  0.052   0.052    0.064    0.064
## 416      Im4 ~~      Im7  1.087 -0.018  -0.018   -0.137   -0.137
## 417     Im17 ~~   COM_A3  1.087  0.031   0.031    0.108    0.108
## 418     PROF =~      Im7  1.079 -0.065  -0.059   -0.049   -0.049
## 419    BRAND =~     Im11  1.044 -0.046  -0.055   -0.048   -0.048
## 420     PROF =~   COM_A1  1.028  0.055   0.050    0.035    0.035
## 421      Im1 ~~   COM_A2  1.000  0.027   0.027    0.108    0.108
## 422      Im6 ~~    SAT_1  0.995  0.022   0.022    0.062    0.062
## 423     Im13 ~~    C_CR3  0.995 -0.046  -0.046   -0.063   -0.063
## 424     Im14 ~~     Im12  0.989 -0.013  -0.013   -0.089   -0.089
## 425   COM_A4 ~~    C_CR3  0.982 -0.063  -0.063   -0.059   -0.059
## 426    SAT_3 ~~   C_REP3  0.980  0.016   0.016    0.049    0.049
## 427      Im1 ~~     Im18  0.980  0.021   0.021    0.104    0.104
## 428   CHOICE =~     Im16  0.965  0.048   0.063    0.052    0.052
## 429   CHOICE =~     Im19  0.965 -0.050  -0.065   -0.058   -0.058
## 430    ATMOS =~      Im2  0.957 -0.032  -0.040   -0.031   -0.031
## 431     Im16 ~~   COM_A3  0.956  0.040   0.040    0.054    0.054
## 432     Im20 ~~     Im18  0.950  0.032   0.032    0.054    0.054
## 433     Im17 ~~   COM_A4  0.902 -0.028  -0.028   -0.101   -0.101
## 434      Im5 ~~      Im2  0.897 -0.023  -0.023   -0.047   -0.047
## 435     Im13 ~~     Im18  0.892 -0.025  -0.025   -0.056   -0.056
## 436    BRAND =~    SAT_3  0.890 -0.037  -0.045   -0.040   -0.040
## 437    ATMOS =~      Im3  0.886  0.024   0.029    0.022    0.022
## 438    ATMOS =~    C_CR3  0.882 -0.050  -0.063   -0.031   -0.031
## 439   CHOICE ~~      SAT  0.882 -0.110  -0.128   -0.128   -0.128
## 440      Im1 ~~      Im2  0.880  1.034   1.034    6.695    6.695
## 441      SAT =~     Im21  0.870  0.051   0.044    0.032    0.032
## 442     Im11 ~~   COM_A2  0.868  0.038   0.038    0.048    0.048
## 443     FOOD =~     Im20  0.862 -0.054  -0.044   -0.029   -0.029
## 444     Im17 ~~   C_REP3  0.860  0.010   0.010    0.090    0.090
## 445      SAT =~      Im1  0.859 -0.049  -0.043   -0.032   -0.032
## 446    ATMOS ~~      SAT  0.859  0.034   0.041    0.041    0.041
## 447      Im7 ~~   COM_A4  0.857  0.031   0.031    0.087    0.087
## 448     Im11 ~~    C_CR4  0.857  0.051   0.051    0.048    0.048
## 449     DECO =~   C_REP2  0.849 -0.014  -0.017   -0.027   -0.027
## 450      Im6 ~~    C_CR4  0.847 -0.041  -0.041   -0.051   -0.051
## 451      Im3 ~~    SAT_1  0.845  0.015   0.015    0.061    0.061
## 452     DECO =~    SAT_2  0.832  0.026   0.033    0.033    0.033
## 453     Im19 ~~    SAT_3  0.832 -0.029  -0.029   -0.052   -0.052
## 454     Im16 ~~   COM_A4  0.828 -0.037  -0.037   -0.052   -0.052
## 455      Im6 ~~   COM_A1  0.825  0.029   0.029    0.048    0.048
## 456      Im6 ~~   C_REP2  0.824  0.010   0.010    0.081    0.081
## 457    BRAND =~      Im1  0.818 -0.039  -0.047   -0.035   -0.035
## 458      Im4 ~~    C_CR3  0.817  0.029   0.029    0.074    0.074
## 459      Im4 ~~   COM_A2  0.807 -0.021  -0.021   -0.071   -0.071
## 460      COI =~    SAT_3  0.791 -0.024  -0.040   -0.035   -0.035
## 461      Im7 ~~    C_CR4  0.785  0.038   0.038    0.082    0.082
## 462    SAT_2 ~~   C_REP3  0.783  0.010   0.010    0.048    0.048
## 463    BRAND =~   COM_A4  0.778 -0.037  -0.045   -0.026   -0.026
## 464     Im16 ~~    SAT_2  0.778  0.024   0.024    0.052    0.052
## 465     Im20 ~~     Im12  0.776  0.026   0.026    0.058    0.058
## 466     PROF =~     Im18  0.772 -0.078  -0.071   -0.051   -0.051
## 467     PROF =~     Im17  0.772  0.079   0.072    0.058    0.058
## 468     FOOD =~    SAT_3  0.770  0.050   0.040    0.036    0.036
## 469      COI =~      Im5  0.767  0.022   0.037    0.028    0.028
## 470     Im17 ~~   C_REP2  0.767  0.009   0.009    0.155    0.155
## 471      Im7 ~~    C_CR1  0.757 -0.035  -0.035   -0.087   -0.087
## 472   FRENCH =~   COM_A1  0.751 -0.042  -0.042   -0.029   -0.029
## 473   CHOICE =~   C_REP2  0.751 -0.012  -0.016   -0.026   -0.026
## 474     Im14 ~~    SAT_1  0.748 -0.010  -0.010   -0.075   -0.075
## 475     Im21 ~~     Im11  0.737 -0.032  -0.032   -0.043   -0.043
## 476      Im3 ~~     Im19  0.732  0.016   0.016    0.055    0.055
## 477     PROF =~     Im11  0.726  0.054   0.049    0.043    0.043
## 478    BRAND =~      Im2  0.725  0.033   0.039    0.031    0.031
## 479     Im12 ~~   COM_A3  0.724 -0.028  -0.028   -0.054   -0.054
## 480      Im1 ~~   C_REP2  0.720  0.008   0.008    0.154    0.154
## 481     Im14 ~~     Im13  0.716  0.012   0.012    0.072    0.072
## 482     Im20 ~~      Im2  0.715 -0.021  -0.021   -0.047   -0.047
## 483      Im2 ~~   C_REP3  0.715  0.009   0.009    0.043    0.043
## 484    BRAND =~   COM_A2  0.713 -0.034  -0.041   -0.026   -0.026
## 485      Im5 ~~    C_CR3  0.707 -0.045  -0.045   -0.045   -0.045
## 486      Im7 ~~   C_REP3  0.706  0.010   0.010    0.071    0.071
## 487      Im5 ~~    C_CR4  0.704  0.044   0.044    0.044    0.044
## 488   COM_A3 ~~    SAT_3  0.702 -0.037  -0.037   -0.044   -0.044
## 489     Im21 ~~     Im17  0.698  0.022   0.022    0.085    0.085
## 490      Im3 ~~    C_CR4  0.696 -0.027  -0.027   -0.049   -0.049
## 491     Im12 ~~   COM_A2  0.654  0.026   0.026    0.052    0.052
## 492     FOOD =~   COM_A2  0.653 -0.047  -0.038   -0.024   -0.024
## 493   COM_A4 ~~   C_REP3  0.652 -0.014  -0.014   -0.043   -0.043
## 494 PRODQUAL =~    SAT_1  0.651 -0.042  -0.029   -0.029   -0.029
## 495     Im21 ~~   C_REP1  0.650 -0.015  -0.015   -0.041   -0.041
## 496      Im4 ~~      Im5  0.638  0.028   0.028    0.099    0.099
## 497    ATMOS =~      Im1  0.638  0.029   0.036    0.027    0.027
## 498    BRAND =~     Im14  0.638  0.015   0.018    0.021    0.021
## 499    BRAND =~     Im10  0.638 -0.015  -0.018   -0.020   -0.020
## 500   FRENCH =~     Im13  0.638 -0.033  -0.033   -0.027   -0.027
## 501    AFCOM =~   C_REP2  0.636 -0.012  -0.014   -0.022   -0.022
## 502      SAT  ~ PRODQUAL  0.629  0.055   0.045    0.045    0.045
## 503 PRODQUAL =~   COM_A3  0.623  0.058   0.041    0.025    0.025
## 504      SAT =~     Im14  0.623  0.020   0.018    0.021    0.021
## 505 PRODQUAL  ~      SAT  0.621 -0.038  -0.047   -0.047   -0.047
## 506    ATMOS =~     Im19  0.620 -0.034  -0.043   -0.038   -0.038
## 507      Im4 ~~     Im10  0.613 -0.008  -0.008   -0.067   -0.067
## 508      Im2 ~~   COM_A4  0.612  0.022   0.022    0.043    0.043
## 509       RI =~      Im1  0.609 -0.046  -0.027   -0.020   -0.020
## 510     Im10 ~~      Im2  0.608 -0.009  -0.009   -0.045   -0.045
## 511     Im10 ~~   COM_A3  0.603 -0.015  -0.015   -0.046   -0.046
## 512    ATMOS =~   COM_A3  0.600  0.039   0.048    0.030    0.030
## 513     Im12 ~~    C_CR1  0.600 -0.031  -0.031   -0.054   -0.054
## 514     FOOD ~~      SAT  0.598  0.017   0.032    0.032    0.032
## 515   COM_A2 ~~    C_CR4  0.598 -0.046  -0.046   -0.044   -0.044
## 516     Im22 ~~     Im13  0.597 -0.024  -0.024   -0.051   -0.051
## 517     Im10 ~~   COM_A1  0.593 -0.014  -0.014   -0.045   -0.045
## 518       RI =~      Im4  0.589 -0.034  -0.020   -0.015   -0.015
## 519     Im21 ~~     Im12  0.585  0.022   0.022    0.047    0.047
## 520      Im7 ~~   C_REP1  0.583  0.011   0.011    0.065    0.065
## 521    SAT_3 ~~    C_CR1  0.582  0.041   0.041    0.044    0.044
## 522      Im4 ~~    C_CR4  0.581  0.024   0.024    0.061    0.061
## 523      Im7 ~~   COM_A3  0.566  0.025   0.025    0.068    0.068
## 524     Im20 ~~      Im7  0.551  0.022   0.022    0.070    0.070
## 525     Im14 ~~     Im22  0.549 -0.012  -0.012   -0.063   -0.063
## 526     Im10 ~~     Im21  0.543 -0.012  -0.012   -0.043   -0.043
## 527      Im4 ~~     Im16  0.541  0.015   0.015    0.059    0.059
## 528     PROF =~     Im22  0.532  0.048   0.043    0.028    0.028
## 529      COI =~      Im3  0.531  0.011   0.019    0.014    0.014
## 530   FRENCH =~     Im21  0.520 -0.034  -0.034   -0.025   -0.025
## 531     Im22 ~~      Im6  0.520  0.022   0.022    0.043    0.043
## 532      Im6 ~~   COM_A3  0.519 -0.025  -0.025   -0.039   -0.039
## 533      Im7 ~~    SAT_1  0.513  0.015   0.015    0.074    0.074
## 534     Im22 ~~     Im16  0.512  0.026   0.026    0.043    0.043
## 535 PRODQUAL =~   C_REP2  0.505  0.020   0.014    0.022    0.022
## 536     Im14 ~~   COM_A4  0.504  0.013   0.013    0.056    0.056
## 537     Im11 ~~     Im18  0.501  0.023   0.023    0.035    0.035
## 538      SAT =~    C_CR3  0.500 -0.053  -0.046   -0.022   -0.022
## 539     Im17 ~~    SAT_3  0.500 -0.019  -0.019   -0.070   -0.070
## 540      Im5 ~~     Im11  0.498  0.026   0.026    0.033    0.033
## 541     Im20 ~~    C_CR3  0.491 -0.040  -0.040   -0.042   -0.042
## 542      Im3 ~~      Im7  0.490 -0.012  -0.012   -0.067   -0.067
## 543     Im10 ~~     Im20  0.488  0.012   0.012    0.043    0.043
## 544   CHOICE =~    C_CR1  0.484 -0.031  -0.041   -0.021   -0.021
## 545     Im14 ~~     Im20  0.479 -0.012  -0.012   -0.055   -0.055
## 546     Im12 ~~      Im2  0.478 -0.013  -0.013   -0.043   -0.043
## 547      Im5 ~~     Im10  0.477 -0.011  -0.011   -0.038   -0.038
## 548     Im21 ~~      Im7  0.471 -0.020  -0.020   -0.061   -0.061
## 549      Im1 ~~    C_CR1  0.468 -0.023  -0.023   -0.082   -0.082
## 550     Im10 ~~    SAT_1  0.467  0.008   0.008    0.047    0.047
## 551      Im2 ~~   COM_A1  0.467 -0.018  -0.018   -0.036   -0.036
## 552 PRODQUAL =~     Im14  0.462  0.027   0.019    0.022    0.022
## 553 PRODQUAL =~     Im10  0.462 -0.026  -0.018   -0.021   -0.021
## 554      Im5 ~~     Im21  0.461 -0.025  -0.025   -0.034   -0.034
## 555     Im12 ~~    SAT_2  0.459 -0.014  -0.014   -0.045   -0.045
## 556      COI =~     Im16  0.453 -0.018  -0.030   -0.025   -0.025
## 557 PRODQUAL =~   C_REP1  0.445  0.022   0.016    0.021    0.021
## 558    BRAND =~     Im19  0.445  0.034   0.040    0.036    0.036
## 559    C_CR1 ~~    C_CR4  0.442 -0.240  -0.240   -0.200   -0.200
## 560     PROF =~      Im3  0.441  0.032   0.029    0.022    0.022
## 561   COM_A1 ~~   C_REP1  0.435 -0.013  -0.013   -0.034   -0.034
## 562    AFCOM =~     Im13  0.435 -0.023  -0.026   -0.021   -0.021
## 563    AFCOM =~    C_CR3  0.434  0.038   0.042    0.020    0.020
## 564     Im19 ~~    SAT_2  0.434  0.015   0.015    0.043    0.043
## 565   CHOICE =~      Im4  0.434 -0.015  -0.019   -0.014   -0.014
## 566     Im12 ~~   C_REP3  0.433 -0.008  -0.008   -0.039   -0.039
## 567     PROF =~      Im6  0.430  0.035   0.032    0.027    0.027
## 568      COI =~   COM_A3  0.429  0.020   0.032    0.020    0.020
## 569   CHOICE =~     Im11  0.426 -0.025  -0.032   -0.028   -0.028
## 570      Im1 ~~     Im16  0.420 -0.016  -0.016   -0.072   -0.072
## 571   CHOICE =~      Im3  0.410 -0.014  -0.019   -0.014   -0.014
## 572    SAT_1 ~~   C_REP2  0.407 -0.006  -0.006   -0.066   -0.066
## 573      Im6 ~~    SAT_3  0.403 -0.020  -0.020   -0.033   -0.033
## 574     Im13 ~~      Im6  0.401  0.016   0.016    0.038    0.038
## 575    AFCOM =~      Im4  0.399 -0.015  -0.016   -0.012   -0.012
## 576       RI =~   COM_A2  0.395 -0.050  -0.029   -0.018   -0.018
## 577    C_CR3 ~~    C_CR4  0.394 -0.226  -0.226   -0.165   -0.165
## 578     Im20 ~~   C_REP1  0.388 -0.012  -0.012   -0.033   -0.033
## 579     Im11 ~~    C_CR3  0.385  0.035   0.035    0.033    0.033
## 580   FRENCH =~    SAT_2  0.383  0.021   0.020    0.020    0.020
## 581     Im12 ~~   C_REP2  0.378  0.007   0.007    0.065    0.065
## 582     Im10 ~~    SAT_3  0.377  0.011   0.011    0.035    0.035
## 583    ATMOS  ~      SAT  0.371 -0.052  -0.036   -0.036   -0.036
## 584     Im13 ~~     Im19  0.371  0.016   0.016    0.040    0.040
## 585     DECO =~    SAT_3  0.370 -0.023  -0.028   -0.025   -0.025
## 586      Im2 ~~      Im7  0.369  0.012   0.012    0.053    0.053
## 587    SAT_2 ~~   C_REP2  0.368  0.006   0.006    0.058    0.058
## 588     Im14 ~~   C_REP2  0.367 -0.004  -0.004   -0.078   -0.078
## 589    AFCOM =~      Im6  0.367  0.022   0.025    0.021    0.021
## 590   COM_A1 ~~    C_CR4  0.359 -0.034  -0.034   -0.033   -0.033
## 591      Im1 ~~    SAT_3  0.354  0.015   0.015    0.061    0.061
## 592     FOOD =~      Im3  0.352 -0.021  -0.017   -0.013   -0.013
## 593      Im6 ~~   COM_A2  0.352  0.020   0.020    0.033    0.033
## 594    ATMOS =~     Im16  0.351 -0.027  -0.033   -0.028   -0.028
## 595      Im5 ~~     Im22  0.351  0.022   0.022    0.033    0.033
## 596 PRODQUAL =~   COM_A1  0.350  0.040   0.028    0.020    0.020
## 597   C_REP2 ~~    C_CR3  0.348  0.012   0.012    0.056    0.056
## 598     Im17 ~~   COM_A2  0.346 -0.017  -0.017   -0.061   -0.061
## 599      Im5 ~~     Im17  0.344  0.015   0.015    0.056    0.056
## 600     Im11 ~~   C_REP3  0.343  0.009   0.009    0.028    0.028
## 601   COM_A3 ~~    SAT_1  0.342  0.018   0.018    0.037    0.037
## 602   CHOICE =~   COM_A4  0.338 -0.022  -0.029   -0.017   -0.017
## 603      Im3 ~~   COM_A2  0.336 -0.014  -0.014   -0.034   -0.034
## 604      Im3 ~~   COM_A1  0.336 -0.013  -0.013   -0.033   -0.033
## 605     Im17 ~~    C_CR1  0.333 -0.021  -0.021   -0.067   -0.067
## 606   FRENCH =~      Im3  0.330 -0.016  -0.016   -0.012   -0.012
## 607      Im6 ~~    C_CR1  0.326  0.024   0.024    0.034    0.034
## 608     Im11 ~~   COM_A1  0.321 -0.022  -0.022   -0.028   -0.028
## 609   COM_A4 ~~    SAT_2  0.316  0.018   0.018    0.034    0.034
## 610    SAT_2 ~~    C_CR1  0.314 -0.021  -0.021   -0.036   -0.036
## 611   FRENCH =~   COM_A4  0.312  0.031   0.030    0.018    0.018
## 612      Im3 ~~     Im13  0.310  0.010   0.010    0.035    0.035
## 613     Im19 ~~    C_CR3  0.309  0.025   0.025    0.035    0.035
## 614   CHOICE =~    C_CR3  0.303 -0.026  -0.035   -0.017   -0.017
## 615      Im3 ~~    SAT_2  0.303 -0.009  -0.009   -0.034   -0.034
## 616     Im13 ~~      Im7  0.303 -0.014  -0.014   -0.055   -0.055
## 617      Im5 ~~   C_REP2  0.302 -0.007  -0.007   -0.046   -0.046
## 618     Im17 ~~      Im7  0.301 -0.012  -0.012   -0.099   -0.099
## 619     Im18 ~~    SAT_1  0.296 -0.012  -0.012   -0.033   -0.033
## 620     Im19 ~~    C_CR1  0.292  0.023   0.023    0.036    0.036
## 621     Im21 ~~     Im13  0.288 -0.017  -0.017   -0.032   -0.032
## 622    AFCOM =~      Im7  0.287 -0.022  -0.024   -0.020   -0.020
## 623    AFCOM =~     Im14  0.284  0.010   0.011    0.013    0.013
## 624   COM_A1 ~~    C_CR1  0.282 -0.028  -0.028   -0.031   -0.031
## 625      Im4 ~~     Im14  0.279  0.005   0.005    0.058    0.058
## 626      Im5 ~~     Im20  0.279  0.020   0.020    0.028    0.028
## 627      COI =~   C_REP3  0.279 -0.006  -0.010   -0.017   -0.017
## 628     Im17 ~~    C_CR3  0.278  0.021   0.021    0.057    0.057
## 629     Im21 ~~   COM_A4  0.277 -0.023  -0.023   -0.029   -0.029
## 630   CHOICE =~     Im17  0.275  0.022   0.028    0.023    0.023
## 631   CHOICE =~     Im18  0.275 -0.021  -0.028   -0.020   -0.020
## 632     Im22 ~~   COM_A2  0.272  0.021   0.021    0.032    0.032
## 633      Im2 ~~    C_CR4  0.271 -0.019  -0.019   -0.029   -0.029
## 634     Im21 ~~     Im16  0.271 -0.019  -0.019   -0.028   -0.028
## 635      Im4 ~~   C_REP3  0.271 -0.005  -0.005   -0.038   -0.038
## 636      COI =~      Im6  0.265 -0.011  -0.018   -0.015   -0.015
## 637      Im7 ~~    SAT_2  0.262 -0.011  -0.011   -0.049   -0.049
## 638   CHOICE =~      Im6  0.256 -0.014  -0.019   -0.016   -0.016
## 639     Im17 ~~    SAT_2  0.247  0.009   0.009    0.054    0.054
## 640     Im20 ~~     Im19  0.247  0.016   0.016    0.031    0.031
## 641      COI =~     Im12  0.243  0.011   0.018    0.016    0.016
## 642     DECO =~    SAT_1  0.242 -0.015  -0.018   -0.018   -0.018
## 643      SAT =~      Im6  0.242  0.022   0.019    0.016    0.016
## 644     Im16 ~~   C_REP1  0.239  0.009   0.009    0.025    0.025
## 645     Im18 ~~   C_REP2  0.237 -0.006  -0.006   -0.043   -0.043
## 646     DECO =~     Im11  0.231  0.019   0.024    0.021    0.021
## 647    SAT_3 ~~   C_REP1  0.230 -0.009  -0.009   -0.024   -0.024
## 648     Im10 ~~     Im19  0.230 -0.007  -0.007   -0.032   -0.032
## 649     DECO =~   COM_A4  0.229  0.019   0.024    0.014    0.014
## 650      Im4 ~~    SAT_1  0.225 -0.007  -0.007   -0.043   -0.043
## 651     Im14 ~~   C_REP1  0.224  0.004   0.004    0.034    0.034
## 652     PROF =~   C_REP2  0.222 -0.011  -0.010   -0.016   -0.016
## 653     Im20 ~~    SAT_3  0.218  0.018   0.018    0.025    0.025
## 654    SAT_3 ~~    C_CR4  0.215  0.026   0.026    0.025    0.025
## 655     Im16 ~~     Im18  0.213 -0.014  -0.014   -0.025   -0.025
## 656     Im11 ~~    SAT_2  0.212 -0.013  -0.013   -0.025   -0.025
## 657     FOOD =~   COM_A4  0.212 -0.028  -0.023   -0.013   -0.013
## 658     PROF =~    SAT_3  0.209 -0.033  -0.030   -0.026   -0.026
## 659     Im21 ~~    SAT_1  0.208  0.012   0.012    0.028    0.028
## 660     Im21 ~~    SAT_2  0.207 -0.012  -0.012   -0.026   -0.026
## 661     Im22 ~~     Im17  0.206  0.012   0.012    0.053    0.053
## 662      Im5 ~~    SAT_1  0.205 -0.012  -0.012   -0.026   -0.026
## 663    AFCOM =~    SAT_3  0.204  0.020   0.023    0.020    0.020
## 664      Im3 ~~   C_REP2  0.199 -0.004  -0.004   -0.043   -0.043
## 665      Im4 ~~   C_REP2  0.198  0.004   0.004    0.058    0.058
## 666      SAT =~   COM_A4  0.197  0.030   0.026    0.015    0.015
## 667 PRODQUAL =~    C_CR3  0.195 -0.041  -0.029   -0.014   -0.014
## 668     Im12 ~~    C_CR3  0.194  0.019   0.019    0.029    0.029
## 669      SAT =~      Im7  0.191  0.021   0.018    0.015    0.015
## 670     Im11 ~~    C_CR1  0.188 -0.023  -0.023   -0.024   -0.024
## 671     Im13 ~~   COM_A1  0.187  0.014   0.014    0.025    0.025
## 672      Im6 ~~   C_REP1  0.185 -0.007  -0.007   -0.022   -0.022
## 673       RI =~     Im20  0.180 -0.036  -0.021   -0.014   -0.014
## 674      Im4 ~~   COM_A1  0.174  0.009   0.009    0.032    0.032
## 675    BRAND =~     Im21  0.174 -0.018  -0.022   -0.016   -0.016
## 676    AFCOM =~     Im18  0.174 -0.015  -0.017   -0.012   -0.012
## 677      Im5 ~~   COM_A3  0.173 -0.017  -0.017   -0.021   -0.021
## 678    AFCOM =~    SAT_1  0.171 -0.015  -0.016   -0.016   -0.016
## 679     Im21 ~~      Im2  0.169  0.010   0.010    0.022    0.022
## 680     Im21 ~~     Im19  0.169 -0.013  -0.013   -0.024   -0.024
## 681     Im16 ~~   C_REP2  0.168 -0.006  -0.006   -0.038   -0.038
## 682   COM_A4 ~~    C_CR1  0.167  0.024   0.024    0.025    0.025
## 683   COM_A2 ~~   C_REP3  0.164 -0.007  -0.007   -0.021   -0.021
## 684     Im20 ~~     Im11  0.164  0.016   0.016    0.021    0.021
## 685     Im22 ~~    C_CR3  0.164  0.023   0.023    0.026    0.026
## 686    ATMOS =~    SAT_1  0.163  0.011   0.014    0.014    0.014
## 687       RI =~     Im18  0.162 -0.027  -0.016   -0.011   -0.011
## 688       RI =~     Im17  0.162  0.027   0.016    0.013    0.013
## 689     DECO ~~    AFCOM  0.161  0.017   0.015    0.015    0.015
## 690      Im1 ~~    C_CR3  0.161 -0.015  -0.015   -0.045   -0.045
## 691     Im16 ~~   COM_A1  0.154 -0.015  -0.015   -0.021   -0.021
## 692     Im12 ~~     Im19  0.151  0.009   0.009    0.027    0.027
## 693     Im10 ~~     Im22  0.151  0.007   0.007    0.026    0.026
## 694     Im22 ~~   COM_A4  0.151  0.017   0.017    0.024    0.024
## 695     Im14 ~~     Im11  0.150  0.006   0.006    0.027    0.027
## 696      Im2 ~~      Im6  0.146 -0.008  -0.008   -0.020   -0.020
## 697     Im14 ~~      Im1  0.145 -0.004  -0.004   -0.058   -0.058
## 698      Im3 ~~   C_REP1  0.142  0.004   0.004    0.021    0.021
## 699       RI =~    C_CR3  0.140  0.041   0.024    0.012    0.012
## 700     Im21 ~~   C_REP2  0.139 -0.005  -0.005   -0.033   -0.033
## 701      SAT =~     Im10  0.138 -0.010  -0.008   -0.010   -0.010
## 702     FOOD =~     Im19  0.138 -0.024  -0.020   -0.017   -0.017
## 703    BRAND =~    SAT_1  0.137 -0.011  -0.013   -0.013   -0.013
## 704      Im4 ~~     Im13  0.137 -0.007  -0.007   -0.032   -0.032
## 705     FOOD =~   COM_A1  0.137 -0.021  -0.017   -0.012   -0.012
## 706     PROF =~    C_CR3  0.136 -0.027  -0.024   -0.012   -0.012
## 707      Im4 ~~     Im20  0.136  0.008   0.008    0.030    0.030
## 708     Im13 ~~    C_CR1  0.134 -0.016  -0.016   -0.024   -0.024
## 709     Im17 ~~      Im6  0.133  0.008   0.008    0.037    0.037
## 710      Im3 ~~    C_CR3  0.132 -0.012  -0.012   -0.022   -0.022
## 711     Im19 ~~      Im6  0.132 -0.009  -0.009   -0.021   -0.021
## 712      Im2 ~~    C_CR3  0.128  0.013   0.013    0.020    0.020
## 713     Im12 ~~     Im18  0.126 -0.009  -0.009   -0.022   -0.022
## 714     FOOD =~      Im4  0.124 -0.013  -0.010   -0.008   -0.008
## 715       RI =~      Im2  0.123  0.018   0.011    0.008    0.008
## 716     Im17 ~~    SAT_1  0.123  0.006   0.006    0.041    0.041
## 717     Im19 ~~    C_CR4  0.122  0.016   0.016    0.021    0.021
## 718     DECO  ~      SAT  0.119 -0.057  -0.040   -0.040   -0.040
## 719      Im1 ~~      Im7  0.119 -0.007  -0.007   -0.063   -0.063
## 720     Im19 ~~      Im7  0.119  0.009   0.009    0.036    0.036
## 721   FRENCH =~     Im17  0.118 -0.014  -0.014   -0.011   -0.011
## 722   FRENCH =~     Im18  0.118  0.014   0.014    0.010    0.010
## 723      Im4 ~~     Im19  0.113 -0.006  -0.006   -0.030   -0.030
## 724     Im16 ~~    SAT_3  0.111  0.012   0.012    0.018    0.018
## 725      SAT =~   C_REP3  0.109  0.007   0.006    0.011    0.011
## 726     FOOD =~     Im21  0.109  0.018   0.015    0.011    0.011
## 727   COM_A3 ~~    C_CR4  0.109 -0.020  -0.020   -0.019   -0.019
## 728     Im18 ~~    C_CR3  0.109 -0.016  -0.016   -0.018   -0.018
## 729    AFCOM =~     Im19  0.108  0.012   0.013    0.012    0.012
## 730    AFCOM =~      Im1  0.108 -0.009  -0.010   -0.008   -0.008
## 731      COI =~   COM_A1  0.107  0.009   0.015    0.010    0.010
## 732      Im3 ~~      Im6  0.106  0.006   0.006    0.019    0.019
## 733     Im21 ~~      Im1  0.105  0.008   0.008    0.034    0.034
## 734     Im21 ~~   COM_A1  0.101  0.012   0.012    0.017    0.017
## 735      COI =~      Im7  0.100 -0.008  -0.013   -0.011   -0.011
## 736     Im17 ~~    C_CR4  0.098  0.012   0.012    0.033    0.033
## 737   CHOICE =~    SAT_3  0.098  0.012   0.016    0.014    0.014
## 738      COI =~     Im14  0.098 -0.004  -0.006   -0.007   -0.007
## 739      COI =~     Im10  0.098  0.004   0.006    0.007    0.007
## 740     FOOD =~     Im22  0.098  0.018   0.015    0.010    0.010
## 741      Im6 ~~   C_REP3  0.097 -0.004  -0.004   -0.016   -0.016
## 742      SAT =~      Im3  0.097  0.010   0.009    0.007    0.007
## 743     Im10 ~~   C_REP2  0.097 -0.002  -0.002   -0.031   -0.031
## 744     Im12 ~~   COM_A1  0.096  0.009   0.009    0.019    0.019
## 745     Im21 ~~    C_CR1  0.096  0.016   0.016    0.018    0.018
## 746       RI =~      Im6  0.094  0.019   0.011    0.010    0.010
## 747   C_REP3 ~~    C_CR1  0.093  0.007   0.007    0.017    0.017
## 748    ATMOS =~      Im6  0.092 -0.010  -0.013   -0.011   -0.011
## 749    ATMOS =~      Im7  0.092  0.012   0.015    0.012    0.012
## 750    AFCOM =~     Im10  0.092 -0.006  -0.006   -0.007   -0.007
## 751     DECO  ~    AFCOM  0.090  0.015   0.013    0.013    0.013
## 752    ATMOS =~    SAT_3  0.086 -0.011  -0.014   -0.012   -0.012
## 753      Im5 ~~   COM_A4  0.085 -0.012  -0.012   -0.015   -0.015
## 754      Im5 ~~     Im18  0.084  0.009   0.009    0.014    0.014
## 755    AFCOM =~     Im17  0.084  0.009   0.010    0.008    0.008
## 756     Im10 ~~   C_REP1  0.082  0.002   0.002    0.016    0.016
## 757      Im4 ~~     Im21  0.080  0.006   0.006    0.022    0.022
## 758   FRENCH =~    C_CR3  0.077 -0.018  -0.018   -0.009   -0.009
## 759     DECO =~     Im21  0.077 -0.011  -0.014   -0.010   -0.010
## 760      Im6 ~~    SAT_2  0.076 -0.006  -0.006   -0.016   -0.016
## 761     Im22 ~~   COM_A3  0.075  0.012   0.012    0.017    0.017
## 762     FOOD =~    C_CR3  0.073 -0.021  -0.017   -0.008   -0.008
## 763     DECO =~     Im19  0.072  0.016   0.020    0.018    0.018
## 764     DECO =~     Im16  0.072 -0.016  -0.019   -0.016   -0.016
## 765      Im3 ~~   C_REP3  0.072  0.002   0.002    0.015    0.015
## 766   FRENCH =~     Im12  0.071 -0.011  -0.010   -0.009   -0.009
## 767      Im4 ~~   C_REP1  0.070 -0.003  -0.003   -0.020   -0.020
## 768      Im7 ~~    C_CR3  0.068 -0.011  -0.011   -0.025   -0.025
## 769     Im11 ~~     Im19  0.067 -0.008  -0.008   -0.014   -0.014
## 770     Im14 ~~    SAT_3  0.066 -0.004  -0.004   -0.019   -0.019
## 771      SAT =~     Im22  0.065 -0.015  -0.013   -0.008   -0.008
## 772      Im5 ~~    C_CR1  0.065  0.013   0.013    0.014    0.014
## 773      Im5 ~~   COM_A1  0.065 -0.010  -0.010   -0.013   -0.013
## 774     Im10 ~~    C_CR3  0.065 -0.006  -0.006   -0.016   -0.016
## 775     PROF =~   COM_A4  0.063 -0.015  -0.014   -0.008   -0.008
## 776      Im5 ~~    SAT_3  0.061 -0.009  -0.009   -0.012   -0.012
## 777     Im21 ~~   COM_A2  0.060  0.010   0.010    0.013    0.013
## 778     Im16 ~~      Im6  0.060 -0.007  -0.007   -0.013   -0.013
## 779     Im20 ~~     Im16  0.059  0.009   0.009    0.014    0.014
## 780     PROF =~     Im21  0.059  0.015   0.013    0.010    0.010
## 781      Im2 ~~     Im19  0.058 -0.005  -0.005   -0.014   -0.014
## 782      Im5 ~~     Im12  0.058  0.007   0.007    0.014    0.014
## 783    ATMOS =~     Im14  0.057  0.004   0.005    0.006    0.006
## 784      Im1 ~~      Im6  0.057 -0.005  -0.005   -0.025   -0.025
## 785    ATMOS =~     Im10  0.057 -0.004  -0.005   -0.006   -0.006
## 786     Im18 ~~   COM_A3  0.057 -0.009  -0.009   -0.013   -0.013
## 787     Im16 ~~   COM_A2  0.056  0.009   0.009    0.013    0.013
## 788      Im4 ~~    SAT_2  0.055 -0.004  -0.004   -0.020   -0.020
## 789     DECO =~   COM_A1  0.055 -0.009  -0.011   -0.007   -0.007
## 790       RI =~    C_CR1  0.054 -0.024  -0.014   -0.007   -0.007
## 791     Im14 ~~   COM_A1  0.054  0.004   0.004    0.017    0.017
## 792     Im10 ~~      Im1  0.054 -0.003  -0.003   -0.027   -0.027
## 793   COM_A2 ~~   C_REP1  0.052  0.005   0.005    0.012    0.012
## 794     Im20 ~~    C_CR1  0.050 -0.012  -0.012   -0.014   -0.014
## 795       RI =~      Im3  0.041  0.009   0.005    0.004    0.004
## 796     Im14 ~~    C_CR3  0.040  0.005   0.005    0.016    0.016
## 797    SAT_1 ~~   C_REP1  0.040  0.003   0.003    0.012    0.012
## 798    BRAND =~    C_CR3  0.039 -0.010  -0.012   -0.006   -0.006
## 799       RI =~    SAT_1  0.038  0.011   0.006    0.006    0.006
## 800    AFCOM =~    C_CR1  0.037  0.010   0.011    0.006    0.006
## 801      Im6 ~~   COM_A4  0.035 -0.007  -0.007   -0.010   -0.010
## 802     FOOD ~~    AFCOM  0.035  0.005   0.007    0.007    0.007
## 803      SAT =~   C_REP2  0.034 -0.004  -0.003   -0.005   -0.005
## 804    SAT_3 ~~   C_REP2  0.034 -0.003  -0.003   -0.016   -0.016
## 805 PRODQUAL =~   COM_A4  0.032 -0.013  -0.009   -0.006   -0.006
## 806     Im20 ~~    C_CR4  0.031 -0.010  -0.010   -0.010   -0.010
## 807     Im18 ~~    SAT_2  0.030  0.004   0.004    0.010    0.010
## 808     Im18 ~~   COM_A4  0.030 -0.006  -0.006   -0.009   -0.009
## 809     DECO =~      Im2  0.026  0.005   0.006    0.005    0.005
## 810     DECO =~      Im1  0.026 -0.006  -0.007   -0.005   -0.005
## 811     Im14 ~~     Im19  0.026  0.002   0.002    0.014    0.014
## 812     PROF  ~    AFCOM  0.026  0.006   0.007    0.007    0.007
## 813    BRAND ~~      SAT  0.025  0.005   0.006    0.006    0.006
## 814   C_REP1 ~~    C_CR4  0.024  0.004   0.004    0.008    0.008
## 815      Im3 ~~    SAT_3  0.024 -0.004  -0.004   -0.009   -0.009
## 816     Im18 ~~    C_CR1  0.022  0.006   0.006    0.009    0.009
## 817     PROF =~     Im10  0.021  0.005   0.005    0.005    0.005
## 818     PROF =~     Im14  0.021 -0.005  -0.005   -0.006   -0.006
## 819     Im19 ~~   C_REP3  0.021 -0.002  -0.002   -0.008   -0.008
## 820     Im19 ~~   COM_A2  0.020 -0.005  -0.005   -0.009   -0.009
## 821       RI =~    SAT_3  0.020  0.011   0.006    0.006    0.006
## 822    BRAND ~~    AFCOM  0.020 -0.006  -0.005   -0.005   -0.005
## 823       RI =~    C_CR4  0.019 -0.015  -0.009   -0.004   -0.004
## 824      Im1 ~~     Im19  0.019 -0.003  -0.003   -0.017   -0.017
## 825      Im1 ~~    C_CR4  0.018 -0.005  -0.005   -0.015   -0.015
## 826     Im12 ~~      Im1  0.018 -0.003  -0.003   -0.017   -0.017
## 827     Im11 ~~    SAT_3  0.018 -0.005  -0.005   -0.006   -0.006
## 828   FRENCH =~      Im4  0.018  0.004   0.004    0.003    0.003
## 829     DECO =~     Im14  0.018  0.003   0.003    0.004    0.004
## 830     DECO =~     Im10  0.018 -0.003  -0.003   -0.004   -0.004
## 831      Im5 ~~   C_REP3  0.015 -0.002  -0.002   -0.006   -0.006
## 832     Im19 ~~   COM_A4  0.014 -0.004  -0.004   -0.007   -0.007
## 833   CHOICE =~   COM_A2  0.013 -0.004  -0.005   -0.003   -0.003
## 834   C_REP2 ~~    C_CR1  0.012  0.002   0.002    0.011    0.011
## 835   C_REP1 ~~    C_CR1  0.012  0.003   0.003    0.006    0.006
## 836    AFCOM =~      Im3  0.012 -0.003  -0.003   -0.002   -0.002
## 837    AFCOM =~     Im22  0.012 -0.006  -0.006   -0.004   -0.004
## 838     Im18 ~~    C_CR4  0.012 -0.005  -0.005   -0.006   -0.006
## 839     FOOD =~     Im17  0.011  0.005   0.004    0.003    0.003
## 840     FOOD =~     Im18  0.011 -0.005  -0.004   -0.003   -0.003
## 841      Im2 ~~    SAT_3  0.010 -0.003  -0.003   -0.005   -0.005
## 842     Im13 ~~    SAT_1  0.010  0.002   0.002    0.007    0.007
## 843    SAT_1 ~~    SAT_2  0.009  0.005   0.005    0.017    0.017
## 844      Im1 ~~   C_REP1  0.009 -0.001  -0.001   -0.009   -0.009
## 845      Im3 ~~     Im16  0.008 -0.002  -0.002   -0.005   -0.005
## 846      COI =~     Im21  0.008  0.002   0.004    0.003    0.003
## 847     Im21 ~~   COM_A3  0.008 -0.004  -0.004   -0.005   -0.005
## 848   CHOICE =~      Im7  0.007  0.003   0.003    0.003    0.003
## 849   COM_A3 ~~    C_CR1  0.007  0.005   0.005    0.005    0.005
## 850   FRENCH  ~    AFCOM  0.006  0.006   0.007    0.007    0.007
## 851     Im11 ~~     Im16  0.006 -0.003  -0.003   -0.004   -0.004
## 852   COM_A2 ~~   C_REP2  0.006  0.001   0.001    0.007    0.007
## 853      Im3 ~~     Im21  0.005 -0.002  -0.002   -0.004   -0.004
## 854    SAT_2 ~~    C_CR4  0.005  0.003   0.003    0.004    0.004
## 855   COM_A4 ~~   C_REP2  0.005 -0.001  -0.001   -0.007   -0.007
## 856 PRODQUAL ~~      SAT  0.004 -0.001  -0.003   -0.003   -0.003
## 857     Im21 ~~      Im6  0.003 -0.002  -0.002   -0.003   -0.003
## 858     Im13 ~~   C_REP3  0.003  0.001   0.001    0.003    0.003
## 859     Im16 ~~     Im17  0.003 -0.001  -0.001   -0.006   -0.006
## 860   COM_A2 ~~    C_CR3  0.003 -0.003  -0.003   -0.003   -0.003
## 861     FOOD =~    SAT_1  0.003 -0.002  -0.002   -0.002   -0.002
## 862   FRENCH =~     Im10  0.002  0.002   0.002    0.002    0.002
## 863   FRENCH =~     Im14  0.002 -0.002  -0.002   -0.002   -0.002
## 864     Im22 ~~    C_CR4  0.002  0.003   0.003    0.003    0.003
## 865     Im16 ~~    C_CR3  0.002 -0.002  -0.002   -0.003   -0.003
## 866 PRODQUAL =~      Im3  0.002  0.002   0.001    0.001    0.001
## 867 PRODQUAL =~     Im21  0.001  0.002   0.002    0.001    0.001
## 868      Im6 ~~    C_CR3  0.001 -0.001  -0.001   -0.002   -0.002
## 869    BRAND =~   C_REP2  0.001  0.000   0.001    0.001    0.001
## 870 PRODQUAL =~    SAT_3  0.000 -0.001  -0.001   -0.001   -0.001
## 871      COI =~     Im18  0.000  0.000  -0.001   -0.001   -0.001
## 872      COI =~     Im17  0.000  0.000   0.001    0.001    0.001
## 873      Im4 ~~    SAT_3  0.000  0.000   0.000   -0.001   -0.001
## 874      Im2 ~~   COM_A2  0.000  0.000   0.000   -0.001   -0.001
## 875     Im13 ~~    C_CR4  0.000  0.001   0.001    0.001    0.001
## 876   FRENCH =~   C_REP3  0.000  0.000   0.000    0.000    0.000
## 877     Im19 ~~   COM_A3  0.000  0.000   0.000    0.001    0.001
## 878     Im18 ~~    SAT_3  0.000  0.000   0.000   -0.001   -0.001
## 879     FOOD =~     Im12  0.000  0.000   0.000    0.000    0.000
## 880   FRENCH =~     Im19  0.000  0.000   0.000    0.000    0.000
## 881    BRAND =~   COM_A1  0.000  0.000   0.000    0.000    0.000
## 882     DECO =~    C_CR3  0.000  0.000   0.000    0.000    0.000
## 883     FOOD =~   C_REP3  0.000  0.000   0.000    0.000    0.000
## 884     Im11 ~~   COM_A4  0.000  0.000   0.000    0.000    0.000
## 885      Im5 ~~     Im13  0.000  0.000   0.000    0.000    0.000
## 886    AFCOM =~     Im21  0.000  0.000   0.000    0.000    0.000

2.4.4 full model

# missing Im8, Im15, Im9

# model_SEM <- "
# DECO =~ Im3 + Im4 + Im5
# FOOD =~ Im10 + Im14
# ATMOS =~ Im20 + Im21 + Im22
# PRODQUAL =~ Im11 + Im12 + Im13
# CHOICE =~ Im1 + Im2  
# PROF =~ Im16 + Im19
# BRAND =~ Im17 + Im18
# FRENCH =~ Im6 + Im7
# 
# AFCOM =~ COM_A1 + COM_A2 + COM_A3 + COM_A4
# SAT =~ SAT_1 + SAT_2 + SAT_3
# RI =~ C_REP1 + C_REP2 + C_REP3
# COI =~ C_CR1 + C_CR3 + C_CR4
# 
# SAT ~ DECO + FOOD + ATMOS + PRODQUAL + CHOICE + PROF + BRAND + FRENCH + Im8 + Im15 + Im9
# AFCOM ~ DECO + FOOD + ATMOS + PRODQUAL + CHOICE + PROF + BRAND + FRENCH + Im8 + Im15 + Im9
# "

# Full model with betas
model_SEM <- "
DECO =~ Im3 + Im4 + Im5
FOOD =~ Im10 + Im14
ATMOS =~ Im20 + Im21 + Im22
PRODQUAL =~ Im11 + Im12 + Im13
CHOICE =~ Im1 + Im2
PROF =~ Im16 + Im19
BRAND =~ Im17 + Im18
FRENCH =~ Im6 + Im7

AFCOM =~ COM_A1 + COM_A2 + COM_A3 + COM_A4
SAT =~ SAT_1 + SAT_2 + SAT_3
RI =~ C_REP1 + C_REP2 + C_REP3
COI =~ C_CR1 + C_CR3 + C_CR4

SAT ~ s1*DECO + s2*FOOD + s3*ATMOS + s4*PRODQUAL + s5*CHOICE + s6*PROF + s7*BRAND + s8*FRENCH + si8*Im8 + si15*Im15 + si9*Im9
AFCOM ~ a1*DECO + a2*FOOD + a3*ATMOS + a4*PRODQUAL + a5*CHOICE + a6*PROF + a7*BRAND + a8*FRENCH + ai8*Im8 + ai15*Im15 + ai9*Im9

RI ~ rs*SAT + ra*AFCOM + r01*DECO + r02*FOOD + r03*ATMOS + r04*PRODQUAL + r05*CHOICE + r06*PROF + r07*BRAND + r08*FRENCH + r0i8*Im8 + r0i15*Im15 + r0i9*Im9
COI ~ cs*SAT + ca*AFCOM + c01*DECO + c02*FOOD + c03*ATMOS + c04*PRODQUAL + c05*CHOICE + c06*PROF + c07*BRAND + c08*FRENCH + c0i8*Im8 + c0i15*Im15 + c0i9*Im9

rss1:= rs*s1
raa1:= ra*a1
css1:= cs*s1
caa1:= ca*a1
DECOtoRI:= r01 + rss1 + raa1
DECOtoCOI:= c01 + css1 + caa1

rss2:= rs*s2
raa2:= ra*a2
css2:= cs*s2
caa2:= ca*a2
FOODtoRI:= r02 + rss2 + raa2
FOODtoCOI:= c02 + css2 + caa2

rss3:= rs*s3
raa3:= ra*a3
css3:= cs*s3
caa3:= ca*a3
ATMOStoRI:= r03 + rss3 + raa3
ATMOStoCOI:= c03 + css3 + caa3

rss4:= rs*s4
raa4:= ra*a4
css4:= cs*s4
caa4:= ca*a4
PQUALtoRI:= r04 + rss4 + raa4
PQUALtoCOI:= c04 + css4 + caa4

rss5:= rs*s5
raa5:= ra*a5
css5:= cs*s5
caa5:= ca*a5
CHOICEtoRI:= r05 + rss5 + raa5
CHOICEtoCOI:= c05 + css5 + caa5

rss6:= rs*s6
raa6:= ra*a6
css6:= cs*s6
caa6:= ca*a6
PROFtoRI:= r06 + rss6 + raa6
PROFtoCOI:= c06 + css6 + caa6

rss7:= rs*s7
raa7:= ra*a7
css7:= cs*s7
caa7:= ca*a7
BRANDtoRI:= r07 + rss7 + raa7
BRANDtoCOI:= c07 + css7 + caa7

rss8:= rs*s8
raa8:= ra*a8
css8:= cs*s8
caa8:= ca*a8
FRENCHtoRI:= r08 + rss8 + raa8
FREMCHtoCOI:= c08 + css8 + caa8
"

# # delete relationships based on regression significance levels
# model_SEM <- "
# DECO =~ Im3 + Im4 + Im5
# FOOD =~ Im10 + Im14
# ATMOS =~ Im20 + Im21 + Im22
# PRODQUAL =~ Im11 + Im12 + Im13
# CHOICE =~ Im1 + Im2  
# PROF =~ Im16 + Im19
# BRAND =~ Im17 + Im18
# FRENCH =~ Im6 + Im7
# 
# AFCOM =~ COM_A1 + COM_A2 + COM_A3 + COM_A4
# SAT =~ SAT_1 + SAT_2 + SAT_3
# RI =~ C_REP1 + C_REP2 + C_REP3
# COI =~ C_CR1 + C_CR3 + C_CR4
# 
# SAT ~ DECO + CHOICE + PROF
# AFCOM ~ ATMOS + PRODQUAL + FRENCH
# 
# RI ~ SAT + AFCOM + ATMOS + PRODQUAL + Im8 + Im9
# COI ~ SAT + AFCOM + ATMOS + PRODQUAL
# "

# # delete relationships based on regression significance levels
# model_SEM <- "
# DECO =~ Im3 + Im4 + Im5
# FOOD =~ Im10 + Im14
# ATMOS =~ Im20 + Im21 + Im22
# PRODQUAL =~ Im11 + Im12 + Im13
# CHOICE =~ Im1 + Im2
# PROF =~ Im16 + Im19
# BRAND =~ Im17 + Im18
# FRENCH =~ Im6 + Im7
# 
# AFCOM =~ COM_A1 + COM_A2 + COM_A3 + COM_A4
# SAT =~ SAT_1 + SAT_2 + SAT_3
# RI =~ C_REP1 + C_REP2 + C_REP3
# COI =~ C_CR1 + C_CR3 + C_CR4
# 
# SAT ~ DECO + CHOICE + PROF
# AFCOM ~ ATMOS + PRODQUAL + FRENCH
# 
# RI ~ SAT + AFCOM + ATMOS + PRODQUAL + Im8 + Im9
# COI ~ SAT + AFCOM + ATMOS + PRODQUAL
# "

# # delete Im8, Im9 move PRODQUAL AFCOM->RI
# model_SEM <- "
# DECO =~ Im3 + Im4 + Im5
# FOOD =~ Im10 + Im14
# ATMOS =~ Im20 + Im21 + Im22
# PRODQUAL =~ Im11 + Im12 + Im13
# CHOICE =~ Im1 + Im2
# PROF =~ Im16 + Im19
# BRAND =~ Im17 + Im18
# FRENCH =~ Im6 + Im7
# 
# AFCOM =~ COM_A1 + COM_A2 + COM_A3 + COM_A4
# SAT =~ SAT_1 + SAT_2 + SAT_3
# RI =~ C_REP2 + C_REP3 + C_REP1
# COI =~ C_CR1 + C_CR3 + C_CR4
# 
# SAT ~ s1*DECO + s5*CHOICE + s6*PROF
# AFCOM ~ a3*ATMOS + a8*FRENCH
# 
# RI ~ rs*SAT + ra*AFCOM + r03*ATMOS + r04*PRODQUAL
# COI ~ cs*SAT + ca*AFCOM + c03*ATMOS
# 
# rss1:= rs*s1
# css1:= cs*s1
# r1:= rss1
# c1:= css1
# 
# raa3:= ra*a3
# caa3:= ca*a3
# r3:= r03 +  raa3
# c3:= c03 + caa3
# 
# rss5:= rs*s5
# css5:= cs*s5
# r5:= rss5 
# c5:= css5
# 
# rss6:= rs*s6
# css6:= cs*s6
# r6:= rss6
# c6:= css6
# 
# raa8:= ra*a8
# caa8:= ca*a8
# r8:= raa8
# c8:= caa8
# "

2.4.5 linear regression

# # linear regression
# lm_SAT_1 <-  lm (model_SAT_1, data = survey) 
# summary(lm_SAT_1)
# # note: lm deletes all missing variables in the Xs! (not in Ys) (see help lavOptions)

2.4.6 path analysis

# path analysis
SEM_fit <- cfa(model_SEM, data=survey, missing="ML")
summary(SEM_fit, fit.measures=TRUE, standardized=TRUE)

## lavaan 0.6.15 ended normally after 176 iterations
## 
##   Estimator                                         ML
##   Optimization method                           NLMINB
##   Number of model parameters                       173
## 
##                                                   Used       Total
##   Number of observations                           523         553
##   Number of missing patterns                       116            
## 
## Model Test User Model:
##                                                       
##   Test statistic                              1863.685
##   Degrees of freedom                               483
##   P-value (Chi-square)                           0.000
## 
## Model Test Baseline Model:
## 
##   Test statistic                             12715.671
##   Degrees of freedom                               592
##   P-value                                        0.000
## 
## User Model versus Baseline Model:
## 
##   Comparative Fit Index (CFI)                    0.886
##   Tucker-Lewis Index (TLI)                       0.860
##                                                       
##   Robust Comparative Fit Index (CFI)             0.888
##   Robust Tucker-Lewis Index (TLI)                0.863
## 
## Loglikelihood and Information Criteria:
## 
##   Loglikelihood user model (H0)             -21205.949
##   Loglikelihood unrestricted model (H1)     -20274.106
##                                                       
##   Akaike (AIC)                               42757.897
##   Bayesian (BIC)                             43494.805
##   Sample-size adjusted Bayesian (SABIC)      42945.662
## 
## Root Mean Square Error of Approximation:
## 
##   RMSEA                                          0.074
##   90 Percent confidence interval - lower         0.070
##   90 Percent confidence interval - upper         0.077
##   P-value H_0: RMSEA <= 0.050                    0.000
##   P-value H_0: RMSEA >= 0.080                    0.002
##                                                       
##   Robust RMSEA                                   0.074
##   90 Percent confidence interval - lower         0.071
##   90 Percent confidence interval - upper         0.078
##   P-value H_0: Robust RMSEA <= 0.050             0.000
##   P-value H_0: Robust RMSEA >= 0.080             0.007
## 
## Standardized Root Mean Square Residual:
## 
##   SRMR                                           0.137
## 
## Parameter Estimates:
## 
##   Standard errors                             Standard
##   Information                                 Observed
##   Observed information based on                Hessian
## 
## Latent Variables:
##                    Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
##   DECO =~                                                               
##     Im3               1.000                               1.247    0.942
##     Im4               1.049    0.025   42.420    0.000    1.309    0.967
##     Im5               0.802    0.034   23.246    0.000    1.000    0.757
##   FOOD =~                                                               
##     Im10              1.000                               0.822    0.927
##     Im14              1.001    0.035   28.365    0.000    0.824    0.954
##   ATMOS =~                                                              
##     Im20              1.000                               1.256    0.845
##     Im21              0.853    0.042   20.438    0.000    1.071    0.783
##     Im22              1.079    0.047   23.137    0.000    1.356    0.886
##   PRODQUAL =~                                                           
##     Im11              1.000                               0.712    0.619
##     Im12              1.385    0.093   14.902    0.000    0.986    0.872
##     Im13              1.450    0.104   13.935    0.000    1.033    0.858
##   CHOICE =~                                                             
##     Im1               1.000                               1.297    0.976
##     Im2               0.886    0.033   26.860    0.000    1.149    0.899
##   PROF =~                                                               
##     Im16              1.000                               0.929    0.768
##     Im19              1.042    0.059   17.538    0.000    0.968    0.854
##   BRAND =~                                                              
##     Im17              1.000                               1.204    0.968
##     Im18              0.996    0.042   23.568    0.000    1.200    0.857
##   FRENCH =~                                                             
##     Im6               1.000                               0.975    0.810
##     Im7               1.192    0.072   16.507    0.000    1.162    0.960
##   AFCOM =~                                                              
##     COM_A1            1.000                               1.116    0.789
##     COM_A2            1.171    0.056   21.068    0.000    1.307    0.829
##     COM_A3            1.154    0.059   19.566    0.000    1.288    0.811
##     COM_A4            1.291    0.063   20.389    0.000    1.441    0.840
##   SAT =~                                                                
##     SAT_1             1.000                               0.845    0.855
##     SAT_2             0.940    0.050   18.659    0.000    0.795    0.807
##     SAT_3             0.841    0.054   15.434    0.000    0.711    0.643
##   RI =~                                                                 
##     C_REP1            1.000                               0.588    0.806
##     C_REP2            0.982    0.045   21.739    0.000    0.577    0.934
##     C_REP3            0.719    0.038   18.680    0.000    0.422    0.761
##   COI =~                                                                
##     C_CR1             1.000                               1.682    0.851
##     C_CR3             1.029    0.052   19.721    0.000    1.730    0.829
##     C_CR4             0.958    0.050   19.155    0.000    1.610    0.805
## 
## Regressions:
##                    Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
##   SAT ~                                                                 
##     DECO      (s1)   -0.098    0.044   -2.242    0.025   -0.144   -0.144
##     FOOD      (s2)    0.077    0.073    1.053    0.292    0.075    0.075
##     ATMOS     (s3)    0.035    0.039    0.882    0.378    0.052    0.052
##     PRODQUA   (s4)   -0.044    0.079   -0.559    0.576   -0.037   -0.037
##     CHOICE    (s5)    0.118    0.042    2.775    0.006    0.181    0.181
##     PROF      (s6)    0.404    0.091    4.454    0.000    0.444    0.444
##     BRAND     (s7)    0.019    0.046    0.422    0.673    0.028    0.028
##     FRENCH    (s8)    0.076    0.059    1.301    0.193    0.088    0.088
##     Im8      (si8)    0.032    0.055    0.595    0.552    0.038    0.040
##     Im15    (si15)    0.057    0.046    1.252    0.210    0.068    0.081
##     Im9      (si9)    0.002    0.033    0.073    0.942    0.003    0.004
##   AFCOM ~                                                               
##     DECO      (a1)   -0.020    0.056   -0.363    0.717   -0.023   -0.023
##     FOOD      (a2)    0.009    0.095    0.092    0.926    0.006    0.006
##     ATMOS     (a3)    0.374    0.054    6.929    0.000    0.421    0.421
##     PRODQUA   (a4)   -0.195    0.104   -1.876    0.061   -0.124   -0.124
##     CHOICE    (a5)    0.086    0.055    1.555    0.120    0.100    0.100
##     PROF      (a6)    0.128    0.112    1.140    0.254    0.107    0.107
##     BRAND     (a7)   -0.016    0.060   -0.272    0.785   -0.018   -0.018
##     FRENCH    (a8)    0.162    0.077    2.099    0.036    0.142    0.142
##     Im8      (ai8)    0.067    0.072    0.932    0.351    0.060    0.063
##     Im15    (ai15)    0.024    0.060    0.401    0.689    0.021    0.026
##     Im9      (ai9)    0.022    0.044    0.508    0.612    0.020    0.027
##   RI ~                                                                  
##     SAT       (rs)    0.191    0.044    4.322    0.000    0.275    0.275
##     AFCOM     (ra)    0.186    0.030    6.163    0.000    0.353    0.353
##     DECO     (r01)    0.007    0.029    0.228    0.820    0.014    0.014
##     FOOD     (r02)    0.009    0.049    0.178    0.858    0.012    0.012
##     ATMOS    (r03)    0.039    0.029    1.344    0.179    0.083    0.083
##     PRODQUA  (r04)    0.116    0.053    2.198    0.028    0.141    0.141
##     CHOICE   (r05)   -0.020    0.028   -0.737    0.461   -0.045   -0.045
##     PROF     (r06)   -0.019    0.061   -0.311    0.756   -0.030   -0.030
##     BRAND    (r07)    0.007    0.030    0.243    0.808    0.015    0.015
##     FRENCH   (r08)   -0.037    0.039   -0.942    0.346   -0.061   -0.061
##     Im8     (r0i8)    0.047    0.037    1.276    0.202    0.079    0.083
##     Im15    (r015)   -0.005    0.030   -0.154    0.878   -0.008   -0.009
##     Im9     (r0i9)   -0.047    0.022   -2.110    0.035   -0.081   -0.109
##   COI ~                                                                 
##     SAT       (cs)   -0.361    0.134   -2.705    0.007   -0.182   -0.182
##     AFCOM     (ca)    0.539    0.093    5.810    0.000    0.358    0.358
##     DECO     (c01)    0.014    0.093    0.155    0.877    0.011    0.011
##     FOOD     (c02)   -0.058    0.154   -0.377    0.706   -0.028   -0.028
##     ATMOS    (c03)    0.146    0.092    1.593    0.111    0.109    0.109
##     PRODQUA  (c04)    0.260    0.168    1.545    0.122    0.110    0.110
##     CHOICE   (c05)   -0.005    0.089   -0.053    0.957   -0.004   -0.004
##     PROF     (c06)   -0.200    0.193   -1.033    0.302   -0.110   -0.110
##     BRAND    (c07)    0.036    0.096    0.376    0.707    0.026    0.026
##     FRENCH   (c08)   -0.107    0.125   -0.862    0.388   -0.062   -0.062
##     Im8     (c0i8)   -0.016    0.116   -0.138    0.890   -0.010   -0.010
##     Im15    (c015)   -0.057    0.098   -0.581    0.561   -0.034   -0.040
##     Im9     (c0i9)   -0.016    0.072   -0.222    0.825   -0.009   -0.013
## 
## Covariances:
##                    Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
##   DECO ~~                                                               
##     FOOD              0.425    0.052    8.167    0.000    0.414    0.414
##     ATMOS             0.738    0.084    8.773    0.000    0.471    0.471
##     PRODQUAL          0.418    0.053    7.874    0.000    0.471    0.471
##     CHOICE            0.731    0.081    8.987    0.000    0.452    0.452
##     PROF              0.767    0.074   10.398    0.000    0.662    0.662
##     BRAND             0.785    0.079    9.990    0.000    0.523    0.523
##     FRENCH            0.409    0.066    6.243    0.000    0.337    0.337
##   FOOD ~~                                                               
##     ATMOS             0.308    0.052    5.887    0.000    0.298    0.298
##     PRODQUAL          0.263    0.035    7.452    0.000    0.448    0.448
##     CHOICE            0.310    0.051    6.054    0.000    0.291    0.291
##     PROF              0.386    0.045    8.516    0.000    0.505    0.505
##     BRAND             0.322    0.048    6.639    0.000    0.325    0.325
##     FRENCH            0.471    0.049    9.658    0.000    0.587    0.587
##   ATMOS ~~                                                              
##     PRODQUAL          0.389    0.055    7.110    0.000    0.435    0.435
##     CHOICE            0.752    0.086    8.722    0.000    0.462    0.462
##     PROF              0.554    0.070    7.941    0.000    0.475    0.475
##     BRAND             0.795    0.083    9.629    0.000    0.526    0.526
##     FRENCH            0.409    0.066    6.222    0.000    0.334    0.334
##   PRODQUAL ~~                                                           
##     CHOICE            0.443    0.055    8.006    0.000    0.480    0.480
##     PROF              0.358    0.045    7.902    0.000    0.541    0.541
##     BRAND             0.481    0.055    8.826    0.000    0.561    0.561
##     FRENCH            0.217    0.039    5.608    0.000    0.313    0.313
##   CHOICE ~~                                                             
##     PROF              0.728    0.074    9.819    0.000    0.605    0.605
##     BRAND             0.805    0.080   10.022    0.000    0.516    0.516
##     FRENCH            0.272    0.061    4.438    0.000    0.215    0.215
##   PROF ~~                                                               
##     BRAND             0.672    0.068    9.851    0.000    0.601    0.601
##     FRENCH            0.333    0.053    6.323    0.000    0.367    0.367
##   BRAND ~~                                                              
##     FRENCH            0.373    0.063    5.938    0.000    0.318    0.318
##  .RI ~~                                                                 
##    .COI              -0.025    0.039   -0.630    0.529   -0.034   -0.034
## 
## Intercepts:
##                    Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
##    .Im3               4.983    0.058   85.740    0.000    4.983    3.762
##    .Im4               4.995    0.059   84.295    0.000    4.995    3.692
##    .Im5               5.049    0.058   86.541    0.000    5.049    3.823
##    .Im10              6.093    0.039  156.804    0.000    6.093    6.865
##    .Im14              6.139    0.038  161.829    0.000    6.139    7.109
##    .Im20              4.705    0.065   72.271    0.000    4.705    3.166
##    .Im21              5.163    0.060   86.178    0.000    5.163    3.775
##    .Im22              4.305    0.067   63.987    0.000    4.305    2.814
##    .Im11              5.652    0.051  111.594    0.000    5.652    4.907
##    .Im12              5.666    0.050  113.818    0.000    5.666    5.010
##    .Im13              5.450    0.053  103.088    0.000    5.450    4.526
##    .Im1               4.808    0.058   82.565    0.000    4.808    3.618
##    .Im2               4.878    0.056   86.961    0.000    4.878    3.814
##    .Im16              5.150    0.053   96.420    0.000    5.150    4.260
##    .Im19              5.158    0.050  103.711    0.000    5.158    4.551
##    .Im17              5.044    0.054   92.559    0.000    5.044    4.056
##    .Im18              4.603    0.062   74.674    0.000    4.603    3.289
##    .Im6               5.821    0.053  110.235    0.000    5.821    4.835
##    .Im7               5.760    0.053  108.103    0.000    5.760    4.761
##    .COM_A1            3.662    0.540    6.781    0.000    3.662    2.590
##    .COM_A2            3.159    0.632    4.997    0.000    3.159    2.005
##    .COM_A3            2.819    0.623    4.525    0.000    2.819    1.774
##    .COM_A4            2.658    0.695    3.823    0.000    2.658    1.550
##    .SAT_1             4.845    0.411   11.786    0.000    4.845    4.902
##    .SAT_2             5.012    0.385   13.012    0.000    5.012    5.088
##    .SAT_3             5.054    0.347   14.556    0.000    5.054    4.573
##    .C_REP1            4.047    0.293   13.797    0.000    4.047    5.552
##    .C_REP2            4.280    0.287   14.889    0.000    4.280    6.927
##    .C_REP3            4.505    0.211   21.340    0.000    4.505    8.120
##    .C_CR1             3.002    0.913    3.289    0.001    3.002    1.519
##    .C_CR3             3.603    0.939    3.836    0.000    3.603    1.726
##    .C_CR4             3.101    0.874    3.547    0.000    3.101    1.549
##     DECO              0.000                               0.000    0.000
##     FOOD              0.000                               0.000    0.000
##     ATMOS             0.000                               0.000    0.000
##     PRODQUAL          0.000                               0.000    0.000
##     CHOICE            0.000                               0.000    0.000
##     PROF              0.000                               0.000    0.000
##     BRAND             0.000                               0.000    0.000
##     FRENCH            0.000                               0.000    0.000
##    .AFCOM             0.000                               0.000    0.000
##    .SAT               0.000                               0.000    0.000
##    .RI                0.000                               0.000    0.000
##    .COI               0.000                               0.000    0.000
## 
## Variances:
##                    Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
##    .Im3               0.198    0.025    8.058    0.000    0.198    0.113
##    .Im4               0.118    0.025    4.775    0.000    0.118    0.064
##    .Im5               0.744    0.050   14.899    0.000    0.744    0.427
##    .Im10              0.111    0.020    5.669    0.000    0.111    0.141
##    .Im14              0.068    0.019    3.580    0.000    0.068    0.091
##    .Im20              0.630    0.059   10.704    0.000    0.630    0.285
##    .Im21              0.724    0.058   12.566    0.000    0.724    0.387
##    .Im22              0.503    0.061    8.276    0.000    0.503    0.215
##    .Im11              0.819    0.057   14.460    0.000    0.819    0.617
##    .Im12              0.306    0.039    7.837    0.000    0.306    0.239
##    .Im13              0.382    0.045    8.579    0.000    0.382    0.264
##    .Im1               0.084    0.049    1.705    0.088    0.084    0.048
##    .Im2               0.314    0.043    7.277    0.000    0.314    0.192
##    .Im16              0.599    0.052   11.542    0.000    0.599    0.409
##    .Im19              0.347    0.045    7.745    0.000    0.347    0.270
##    .Im17              0.097    0.046    2.105    0.035    0.097    0.063
##    .Im18              0.520    0.056    9.255    0.000    0.520    0.265
##    .Im6               0.498    0.057    8.699    0.000    0.498    0.344
##    .Im7               0.113    0.068    1.666    0.096    0.113    0.077
##    .COM_A1            0.754    0.060   12.580    0.000    0.754    0.377
##    .COM_A2            0.776    0.067   11.552    0.000    0.776    0.312
##    .COM_A3            0.866    0.071   12.145    0.000    0.866    0.343
##    .COM_A4            0.863    0.077   11.218    0.000    0.863    0.294
##    .SAT_1             0.262    0.034    7.705    0.000    0.262    0.268
##    .SAT_2             0.338    0.034    9.853    0.000    0.338    0.349
##    .SAT_3             0.716    0.053   13.634    0.000    0.716    0.586
##    .C_REP1            0.186    0.016   11.320    0.000    0.186    0.350
##    .C_REP2            0.049    0.011    4.657    0.000    0.049    0.128
##    .C_REP3            0.129    0.009   13.622    0.000    0.129    0.420
##    .C_CR1             1.076    0.119    9.063    0.000    1.076    0.276
##    .C_CR3             1.362    0.134   10.152    0.000    1.362    0.313
##    .C_CR4             1.412    0.128   11.028    0.000    1.412    0.353
##     DECO              1.556    0.110   14.096    0.000    1.000    1.000
##     FOOD              0.676    0.052   13.094    0.000    1.000    1.000
##     ATMOS             1.578    0.138   11.424    0.000    1.000    1.000
##     PRODQUAL          0.508    0.070    7.277    0.000    1.000    1.000
##     CHOICE            1.681    0.120   14.033    0.000    1.000    1.000
##     PROF              0.863    0.090    9.550    0.000    1.000    1.000
##     BRAND             1.449    0.106   13.646    0.000    1.000    1.000
##     FRENCH            0.951    0.097    9.789    0.000    1.000    1.000
##    .AFCOM             0.884    0.090    9.820    0.000    0.710    0.710
##    .SAT               0.459    0.049    9.461    0.000    0.642    0.642
##    .RI                0.232    0.022   10.542    0.000    0.672    0.672
##    .COI               2.331    0.219   10.631    0.000    0.824    0.824
## 
## Defined Parameters:
##                    Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
##     rss1             -0.019    0.009   -1.984    0.047   -0.040   -0.040
##     raa1             -0.004    0.010   -0.362    0.717   -0.008   -0.008
##     css1              0.035    0.020    1.737    0.082    0.026    0.026
##     caa1             -0.011    0.030   -0.362    0.717   -0.008   -0.008
##     DECOtoRI         -0.016    0.031   -0.517    0.605   -0.034   -0.034
##     DECOtoCOI         0.039    0.095    0.408    0.683    0.029    0.029
##     rss2              0.015    0.014    1.022    0.307    0.021    0.021
##     raa2              0.002    0.018    0.092    0.926    0.002    0.002
##     css2             -0.028    0.028   -0.979    0.327   -0.014   -0.014
##     caa2              0.005    0.051    0.092    0.926    0.002    0.002
##     FOODtoRI          0.025    0.052    0.479    0.632    0.035    0.035
##     FOODtoCOI        -0.081    0.161   -0.504    0.614   -0.040   -0.040
##     rss3              0.007    0.008    0.867    0.386    0.014    0.014
##     raa3              0.069    0.015    4.716    0.000    0.148    0.148
##     css3             -0.013    0.015   -0.834    0.404   -0.009   -0.009
##     caa3              0.201    0.044    4.567    0.000    0.150    0.150
##     ATMOStoRI         0.115    0.029    3.970    0.000    0.246    0.246
##     ATMOStoCOI        0.335    0.088    3.801    0.000    0.250    0.250
##     rss4             -0.008    0.015   -0.553    0.580   -0.010   -0.010
##     raa4             -0.036    0.020   -1.786    0.074   -0.044   -0.044
##     css4              0.016    0.029    0.549    0.583    0.007    0.007
##     caa4             -0.105    0.059   -1.779    0.075   -0.044   -0.044
##     PQUALtoRI         0.072    0.056    1.283    0.199    0.087    0.087
##     PQUALtoCOI        0.171    0.173    0.984    0.325    0.072    0.072
##     rss5              0.023    0.010    2.369    0.018    0.050    0.050
##     raa5              0.016    0.011    1.509    0.131    0.035    0.035
##     css5             -0.043    0.022   -1.930    0.054   -0.033   -0.033
##     caa5              0.046    0.031    1.510    0.131    0.036    0.036
##     CHOICEtoRI        0.018    0.030    0.612    0.541    0.040    0.040
##     CHOICEtoCOI      -0.001    0.093   -0.013    0.990   -0.001   -0.001
##     rss6              0.077    0.025    3.070    0.002    0.122    0.122
##     raa6              0.024    0.021    1.123    0.262    0.038    0.038
##     css6             -0.146    0.062   -2.350    0.019   -0.081   -0.081
##     caa6              0.069    0.062    1.112    0.266    0.038    0.038
##     PROFtoRI          0.082    0.061    1.344    0.179    0.130    0.130
##     PROFtoCOI        -0.277    0.185   -1.492    0.136   -0.153   -0.153
##     rss7              0.004    0.009    0.419    0.675    0.008    0.008
##     raa7             -0.003    0.011   -0.272    0.786   -0.006   -0.006
##     css7             -0.007    0.017   -0.417    0.677   -0.005   -0.005
##     caa7             -0.009    0.032   -0.272    0.786   -0.006   -0.006
##     BRANDtoRI         0.008    0.032    0.247    0.805    0.016    0.016
##     BRANDtoCOI        0.020    0.101    0.203    0.839    0.015    0.015
##     rss8              0.015    0.012    1.246    0.213    0.024    0.024
##     raa8              0.030    0.015    1.990    0.047    0.050    0.050
##     css8             -0.028    0.023   -1.178    0.239   -0.016   -0.016
##     caa8              0.088    0.044    1.973    0.048    0.051    0.051
##     FRENCHtoRI        0.008    0.042    0.194    0.846    0.013    0.013
##     FREMCHtoCOI      -0.047    0.129   -0.368    0.713   -0.028   -0.028

# note: cfa deletes all missing variables in the Xs! (not in Ys) (see help lavOptions)

2.4.6.1 Discussion of global fit measures

Chi square: p-value > 0.05

RMSEA RMSEA <= 0.05 Good fit 0.05 < RMSEA <= 0.08 Acceptable fit 0.08 < RMSEA <= 0.10 Bad fit RMSEA > 0.1 Unacceptable fit

CFI CFI < 0.90 definitely reject model 0.90 < CFI < 0.95 high underrejection rates for misspecified models CFI > 0.95 accept model

2.4.6.2 local fit measures

# semPaths(SEM_fit, what = "path", whatLabels = "std", style = "mx",
#          rotation = 2, layout = "tree3", mar = c(1, 2, 1, 2), 
#          nCharNodes = 7,shapeMan = "rectangle", sizeMan = 8, sizeMan2 = 5, 
#          curvePivot=TRUE, edge.label.cex = 1.2, edge.color = "skyblue4")


# semPaths(SEM_fit, what = "col", whatLabels = "par", style = "ram",
#          rotation = 2, layout = "tree3", 
#          mar = c(1, 2, 1, 2), #margins
#          nCharNodes = 7,
#          shapeMan = "rectangle", # variable shape
#          sizeMan = 4, # variable shape size
#          sizeMan2 = 3, # variable shape vertical stretch
#          # structural = T, # don't plot image variables (manifests)
#          sizeInt = 1, # intercept size
#          intercepts = F, # don't include intercepts
#          sizeLat = 5, #factor size
#          asize = 2, # arrow size
#          curvePivot=T, # edge broken curve
#          edge.label.cex = .5, # edge label size
#          # edge.color = "skyblue4",
#          # levels= c(1,2,7,8,9,10),
#          groups = "latents",
#          cut = .5 #cutoff for edges,
#          )

semPaths(SEM_fit, what = "est", whatLabels = "std", style = "mx",
         rotation = 2, layout = "tree3", 
         mar = c(1, 2, 1, 2), #margins
         nCharNodes = 7,
         shapeMan = "rectangle", # variable shape
         sizeMan = 4, # variable shape size
         sizeMan2 = 3, # variable shape vertical stretch
         structural = T, # don't plot image variables (manifests)
         sizeInt = 1, # intercept size
         intercepts = F, # don't include intercepts
         sizeLat = 5, #factor size
         asize = 2, # arrow size
         curvePivot=T, # edge broken curve
         edge.label.cex = .6, # edge label size
         edge.color = "skyblue4",
         # levels= c(1,2,7,8,9,10),
         # groups = "latents",
         cut = .4 #cutoff for edges,
         )

lambda = inspect(SEM_fit, what="std")$lambda
theta = inspect(SEM_fit, what="std")$theta

# create lambda matrix with ones instead of std.all
ones <- lambda
ones[ones>0] <- 1

# a matrix with dimensions of lambda matrix but with lambdas replaced by thetas
theta_lb <- theta %*% ones

2.4.6.2.1 Indicator reliability criterion (Individual Item Reliability)

# JONATHAN
# calculate indicator reliabilities (should be larger than 0.4)
indicrel <- lambda^2/(lambda^2 + theta_lb)
# indicrel

# replace all values satisfying condition with NaN for visibility
indicrel_fail <- indicrel
indicrel_fail[indicrel_fail>.4] <- NaN
indicrel_fail

##        DECO FOOD ATMOS PRODQU CHOICE PROF BRAND FRENCH AFCOM SAT  RI COI Im8
## Im3     NaN  NaN   NaN    NaN    NaN  NaN   NaN    NaN   NaN NaN NaN NaN NaN
## Im4     NaN  NaN   NaN    NaN    NaN  NaN   NaN    NaN   NaN NaN NaN NaN NaN
## Im5     NaN  NaN   NaN    NaN    NaN  NaN   NaN    NaN   NaN NaN NaN NaN NaN
## Im10    NaN  NaN   NaN    NaN    NaN  NaN   NaN    NaN   NaN NaN NaN NaN NaN
## Im14    NaN  NaN   NaN    NaN    NaN  NaN   NaN    NaN   NaN NaN NaN NaN NaN
## Im20    NaN  NaN   NaN    NaN    NaN  NaN   NaN    NaN   NaN NaN NaN NaN NaN
## Im21    NaN  NaN   NaN    NaN    NaN  NaN   NaN    NaN   NaN NaN NaN NaN NaN
## Im22    NaN  NaN   NaN    NaN    NaN  NaN   NaN    NaN   NaN NaN NaN NaN NaN
## Im11    NaN  NaN   NaN  0.383    NaN  NaN   NaN    NaN   NaN NaN NaN NaN NaN
## Im12    NaN  NaN   NaN    NaN    NaN  NaN   NaN    NaN   NaN NaN NaN NaN NaN
## Im13    NaN  NaN   NaN    NaN    NaN  NaN   NaN    NaN   NaN NaN NaN NaN NaN
## Im1     NaN  NaN   NaN    NaN    NaN  NaN   NaN    NaN   NaN NaN NaN NaN NaN
## Im2     NaN  NaN   NaN    NaN    NaN  NaN   NaN    NaN   NaN NaN NaN NaN NaN
## Im16    NaN  NaN   NaN    NaN    NaN  NaN   NaN    NaN   NaN NaN NaN NaN NaN
## Im19    NaN  NaN   NaN    NaN    NaN  NaN   NaN    NaN   NaN NaN NaN NaN NaN
## Im17    NaN  NaN   NaN    NaN    NaN  NaN   NaN    NaN   NaN NaN NaN NaN NaN
## Im18    NaN  NaN   NaN    NaN    NaN  NaN   NaN    NaN   NaN NaN NaN NaN NaN
## Im6     NaN  NaN   NaN    NaN    NaN  NaN   NaN    NaN   NaN NaN NaN NaN NaN
## Im7     NaN  NaN   NaN    NaN    NaN  NaN   NaN    NaN   NaN NaN NaN NaN NaN
## COM_A1  NaN  NaN   NaN    NaN    NaN  NaN   NaN    NaN   NaN NaN NaN NaN NaN
## COM_A2  NaN  NaN   NaN    NaN    NaN  NaN   NaN    NaN   NaN NaN NaN NaN NaN
## COM_A3  NaN  NaN   NaN    NaN    NaN  NaN   NaN    NaN   NaN NaN NaN NaN NaN
## COM_A4  NaN  NaN   NaN    NaN    NaN  NaN   NaN    NaN   NaN NaN NaN NaN NaN
## SAT_1   NaN  NaN   NaN    NaN    NaN  NaN   NaN    NaN   NaN NaN NaN NaN NaN
## SAT_2   NaN  NaN   NaN    NaN    NaN  NaN   NaN    NaN   NaN NaN NaN NaN NaN
## SAT_3   NaN  NaN   NaN    NaN    NaN  NaN   NaN    NaN   NaN NaN NaN NaN NaN
## C_REP1  NaN  NaN   NaN    NaN    NaN  NaN   NaN    NaN   NaN NaN NaN NaN NaN
## C_REP2  NaN  NaN   NaN    NaN    NaN  NaN   NaN    NaN   NaN NaN NaN NaN NaN
## C_REP3  NaN  NaN   NaN    NaN    NaN  NaN   NaN    NaN   NaN NaN NaN NaN NaN
## C_CR1   NaN  NaN   NaN    NaN    NaN  NaN   NaN    NaN   NaN NaN NaN NaN NaN
## C_CR3   NaN  NaN   NaN    NaN    NaN  NaN   NaN    NaN   NaN NaN NaN NaN NaN
## C_CR4   NaN  NaN   NaN    NaN    NaN  NaN   NaN    NaN   NaN NaN NaN NaN NaN
## Im8     NaN  NaN   NaN    NaN    NaN  NaN   NaN    NaN   NaN NaN NaN NaN NaN
## Im15    NaN  NaN   NaN    NaN    NaN  NaN   NaN    NaN   NaN NaN NaN NaN NaN
## Im9     NaN  NaN   NaN    NaN    NaN  NaN   NaN    NaN   NaN NaN NaN NaN NaN
##        Im15 Im9
## Im3     NaN NaN
## Im4     NaN NaN
## Im5     NaN NaN
## Im10    NaN NaN
## Im14    NaN NaN
## Im20    NaN NaN
## Im21    NaN NaN
## Im22    NaN NaN
## Im11    NaN NaN
## Im12    NaN NaN
## Im13    NaN NaN
## Im1     NaN NaN
## Im2     NaN NaN
## Im16    NaN NaN
## Im19    NaN NaN
## Im17    NaN NaN
## Im18    NaN NaN
## Im6     NaN NaN
## Im7     NaN NaN
## COM_A1  NaN NaN
## COM_A2  NaN NaN
## COM_A3  NaN NaN
## COM_A4  NaN NaN
## SAT_1   NaN NaN
## SAT_2   NaN NaN
## SAT_3   NaN NaN
## C_REP1  NaN NaN
## C_REP2  NaN NaN
## C_REP3  NaN NaN
## C_CR1   NaN NaN
## C_CR3   NaN NaN
## C_CR4   NaN NaN
## Im8     NaN NaN
## Im15    NaN NaN
## Im9     NaN NaN

# FERESHTEH
#Local Fit

std.loadings<- inspect(SEM_fit, what="std")$lambda
check=std.loadings
check[check>0] <- 1
std.loadings[std.loadings==0] <- NA
std.loadings2 <- std.loadings^2
std.theta<- inspect(SEM_fit, what="std")$theta

#Individual item Reliability
IIR=std.loadings2/(colSums(std.theta)+std.loadings2)
IIR

##         DECO  FOOD ATMOS PRODQU CHOICE  PROF BRAND FRENCH AFCOM   SAT    RI
## Im3    0.887    NA    NA     NA     NA    NA    NA     NA    NA    NA    NA
## Im4    0.936    NA    NA     NA     NA    NA    NA     NA    NA    NA    NA
## Im5    0.573    NA    NA     NA     NA    NA    NA     NA    NA    NA    NA
## Im10      NA 0.859    NA     NA     NA    NA    NA     NA    NA    NA    NA
## Im14      NA 0.909    NA     NA     NA    NA    NA     NA    NA    NA    NA
## Im20      NA    NA 0.715     NA     NA    NA    NA     NA    NA    NA    NA
## Im21      NA    NA 0.613     NA     NA    NA    NA     NA    NA    NA    NA
## Im22      NA    NA 0.785     NA     NA    NA    NA     NA    NA    NA    NA
## Im11      NA    NA    NA  0.383     NA    NA    NA     NA    NA    NA    NA
## Im12      NA    NA    NA  0.761     NA    NA    NA     NA    NA    NA    NA
## Im13      NA    NA    NA  0.736     NA    NA    NA     NA    NA    NA    NA
## Im1       NA    NA    NA     NA  0.952    NA    NA     NA    NA    NA    NA
## Im2       NA    NA    NA     NA  0.808    NA    NA     NA    NA    NA    NA
## Im16      NA    NA    NA     NA     NA 0.591    NA     NA    NA    NA    NA
## Im19      NA    NA    NA     NA     NA 0.730    NA     NA    NA    NA    NA
## Im17      NA    NA    NA     NA     NA    NA 0.937     NA    NA    NA    NA
## Im18      NA    NA    NA     NA     NA    NA 0.735     NA    NA    NA    NA
## Im6       NA    NA    NA     NA     NA    NA    NA  0.656    NA    NA    NA
## Im7       NA    NA    NA     NA     NA    NA    NA  0.923    NA    NA    NA
## COM_A1    NA    NA    NA     NA     NA    NA    NA     NA 0.623    NA    NA
## COM_A2    NA    NA    NA     NA     NA    NA    NA     NA 0.688    NA    NA
## COM_A3    NA    NA    NA     NA     NA    NA    NA     NA 0.657    NA    NA
## COM_A4    NA    NA    NA     NA     NA    NA    NA     NA 0.706    NA    NA
## SAT_1     NA    NA    NA     NA     NA    NA    NA     NA    NA 0.732    NA
## SAT_2     NA    NA    NA     NA     NA    NA    NA     NA    NA 0.651    NA
## SAT_3     NA    NA    NA     NA     NA    NA    NA     NA    NA 0.414    NA
## C_REP1    NA    NA    NA     NA     NA    NA    NA     NA    NA    NA 0.650
## C_REP2    NA    NA    NA     NA     NA    NA    NA     NA    NA    NA 0.872
## C_REP3    NA    NA    NA     NA     NA    NA    NA     NA    NA    NA 0.580
## C_CR1     NA    NA    NA     NA     NA    NA    NA     NA    NA    NA    NA
## C_CR3     NA    NA    NA     NA     NA    NA    NA     NA    NA    NA    NA
## C_CR4     NA    NA    NA     NA     NA    NA    NA     NA    NA    NA    NA
## Im8       NA    NA    NA     NA     NA    NA    NA     NA    NA    NA    NA
## Im15      NA    NA    NA     NA     NA    NA    NA     NA    NA    NA    NA
## Im9       NA    NA    NA     NA     NA    NA    NA     NA    NA    NA    NA
##          COI Im8 Im15 Im9
## Im3       NA  NA   NA  NA
## Im4       NA  NA   NA  NA
## Im5       NA  NA   NA  NA
## Im10      NA  NA   NA  NA
## Im14      NA  NA   NA  NA
## Im20      NA  NA   NA  NA
## Im21      NA  NA   NA  NA
## Im22      NA  NA   NA  NA
## Im11      NA  NA   NA  NA
## Im12      NA  NA   NA  NA
## Im13      NA  NA   NA  NA
## Im1       NA  NA   NA  NA
## Im2       NA  NA   NA  NA
## Im16      NA  NA   NA  NA
## Im19      NA  NA   NA  NA
## Im17      NA  NA   NA  NA
## Im18      NA  NA   NA  NA
## Im6       NA  NA   NA  NA
## Im7       NA  NA   NA  NA
## COM_A1    NA  NA   NA  NA
## COM_A2    NA  NA   NA  NA
## COM_A3    NA  NA   NA  NA
## COM_A4    NA  NA   NA  NA
## SAT_1     NA  NA   NA  NA
## SAT_2     NA  NA   NA  NA
## SAT_3     NA  NA   NA  NA
## C_REP1    NA  NA   NA  NA
## C_REP2    NA  NA   NA  NA
## C_REP3    NA  NA   NA  NA
## C_CR1  0.724  NA   NA  NA
## C_CR3  0.687  NA   NA  NA
## C_CR4  0.647  NA   NA  NA
## Im8       NA   1   NA  NA
## Im15      NA  NA    1  NA
## Im9       NA  NA   NA   1

2.4.6.2.2 Construct reliability criterion

# JONATHAN
# calculate construct reliability (should be above .6)
constrrel <- (t(lambda) %*% ones)^2 / ((t(lambda) %*% ones)^2 + t(theta_lb) %*% ones )
# constrrel

# replace all values satisfying condition with NaN for visibility
constrrel_fail <- constrrel
constrrel_fail[constrrel_fail>.6] <- NaN
constrrel_fail

##          DECO FOOD ATMOS PRODQUAL CHOICE PROF BRAND FRENCH AFCOM SAT  RI COI
## DECO      NaN  NaN   NaN      NaN    NaN  NaN   NaN    NaN   NaN NaN NaN NaN
## FOOD      NaN  NaN   NaN      NaN    NaN  NaN   NaN    NaN   NaN NaN NaN NaN
## ATMOS     NaN  NaN   NaN      NaN    NaN  NaN   NaN    NaN   NaN NaN NaN NaN
## PRODQUAL  NaN  NaN   NaN      NaN    NaN  NaN   NaN    NaN   NaN NaN NaN NaN
## CHOICE    NaN  NaN   NaN      NaN    NaN  NaN   NaN    NaN   NaN NaN NaN NaN
## PROF      NaN  NaN   NaN      NaN    NaN  NaN   NaN    NaN   NaN NaN NaN NaN
## BRAND     NaN  NaN   NaN      NaN    NaN  NaN   NaN    NaN   NaN NaN NaN NaN
## FRENCH    NaN  NaN   NaN      NaN    NaN  NaN   NaN    NaN   NaN NaN NaN NaN
## AFCOM     NaN  NaN   NaN      NaN    NaN  NaN   NaN    NaN   NaN NaN NaN NaN
## SAT       NaN  NaN   NaN      NaN    NaN  NaN   NaN    NaN   NaN NaN NaN NaN
## RI        NaN  NaN   NaN      NaN    NaN  NaN   NaN    NaN   NaN NaN NaN NaN
## COI       NaN  NaN   NaN      NaN    NaN  NaN   NaN    NaN   NaN NaN NaN NaN
## Im8       NaN  NaN   NaN      NaN    NaN  NaN   NaN    NaN   NaN NaN NaN NaN
## Im15      NaN  NaN   NaN      NaN    NaN  NaN   NaN    NaN   NaN NaN NaN NaN
## Im9       NaN  NaN   NaN      NaN    NaN  NaN   NaN    NaN   NaN NaN NaN NaN
##          Im8 Im15 Im9
## DECO     NaN  NaN NaN
## FOOD     NaN  NaN NaN
## ATMOS    NaN  NaN NaN
## PRODQUAL NaN  NaN NaN
## CHOICE   NaN  NaN NaN
## PROF     NaN  NaN NaN
## BRAND    NaN  NaN NaN
## FRENCH   NaN  NaN NaN
## AFCOM    NaN  NaN NaN
## SAT      NaN  NaN NaN
## RI       NaN  NaN NaN
## COI      NaN  NaN NaN
## Im8      NaN  NaN NaN
## Im15     NaN  NaN NaN
## Im9      NaN  NaN NaN

# FERESHTEH
#Composite/Construct Reliability
sum.std.loadings<-colSums(std.loadings, na.rm=TRUE)^2
sum.std.theta<-rowSums(std.theta)
sum.std.theta=check*sum.std.theta
CR=sum.std.loadings/(sum.std.loadings+colSums(sum.std.theta))
CR

##      DECO      FOOD     ATMOS  PRODQUAL    CHOICE      PROF     BRAND    FRENCH 
## 0.9216860 0.9384670 0.8769271 0.8312694 0.9361559 0.7947441 0.9102652 0.8815253 
##     AFCOM       SAT        RI       COI       Im8      Im15       Im9 
## 0.8896815 0.8154708 0.8744045 0.8677621 1.0000000 1.0000000 1.0000000

2.4.6.2.3 Average Variance Extracted criterion

# JONATHAN
# calculate Average Variance Extracted (should be above .5)
AVE <- (t(lambda) %*% lambda) / (t(lambda) %*% lambda + t(theta_lb) %*% ones )
# avgvar

# replace all values satisfying condition with NaN for visibility
AVE_fail <- AVE
AVE_fail[AVE_fail>.5] <- NaN
AVE_fail

##          DECO FOOD ATMOS PRODQUAL CHOICE PROF BRAND FRENCH AFCOM SAT  RI COI
## DECO      NaN  NaN   NaN      NaN    NaN  NaN   NaN    NaN   NaN NaN NaN NaN
## FOOD      NaN  NaN   NaN      NaN    NaN  NaN   NaN    NaN   NaN NaN NaN NaN
## ATMOS     NaN  NaN   NaN      NaN    NaN  NaN   NaN    NaN   NaN NaN NaN NaN
## PRODQUAL  NaN  NaN   NaN      NaN    NaN  NaN   NaN    NaN   NaN NaN NaN NaN
## CHOICE    NaN  NaN   NaN      NaN    NaN  NaN   NaN    NaN   NaN NaN NaN NaN
## PROF      NaN  NaN   NaN      NaN    NaN  NaN   NaN    NaN   NaN NaN NaN NaN
## BRAND     NaN  NaN   NaN      NaN    NaN  NaN   NaN    NaN   NaN NaN NaN NaN
## FRENCH    NaN  NaN   NaN      NaN    NaN  NaN   NaN    NaN   NaN NaN NaN NaN
## AFCOM     NaN  NaN   NaN      NaN    NaN  NaN   NaN    NaN   NaN NaN NaN NaN
## SAT       NaN  NaN   NaN      NaN    NaN  NaN   NaN    NaN   NaN NaN NaN NaN
## RI        NaN  NaN   NaN      NaN    NaN  NaN   NaN    NaN   NaN NaN NaN NaN
## COI       NaN  NaN   NaN      NaN    NaN  NaN   NaN    NaN   NaN NaN NaN NaN
## Im8       NaN  NaN   NaN      NaN    NaN  NaN   NaN    NaN   NaN NaN NaN NaN
## Im15      NaN  NaN   NaN      NaN    NaN  NaN   NaN    NaN   NaN NaN NaN NaN
## Im9       NaN  NaN   NaN      NaN    NaN  NaN   NaN    NaN   NaN NaN NaN NaN
##          Im8 Im15 Im9
## DECO     NaN  NaN NaN
## FOOD     NaN  NaN NaN
## ATMOS    NaN  NaN NaN
## PRODQUAL NaN  NaN NaN
## CHOICE   NaN  NaN NaN
## PROF     NaN  NaN NaN
## BRAND    NaN  NaN NaN
## FRENCH   NaN  NaN NaN
## AFCOM    NaN  NaN NaN
## SAT      NaN  NaN NaN
## RI       NaN  NaN NaN
## COI      NaN  NaN NaN
## Im8      NaN  NaN NaN
## Im15     NaN  NaN NaN
## Im9      NaN  NaN NaN

# FERESHTEH
#Average Variance Extracted 
std.loadings<- inspect(SEM_fit, what="std")$lambda
std.loadings <- std.loadings^2
AVE_fshteh=colSums(std.loadings)/(colSums(sum.std.theta)+colSums(std.loadings))
AVE_fshteh

##      DECO      FOOD     ATMOS  PRODQUAL    CHOICE      PROF     BRAND    FRENCH 
## 0.7986537 0.8840885 0.7042434 0.6266576 0.8801527 0.6600238 0.8358149 0.7893477 
##     AFCOM       SAT        RI       COI       Im8      Im15       Im9 
## 0.6685779 0.5989777 0.7004635 0.6863754 1.0000000 1.0000000 1.0000000

2.4.6.2.4 Fornell-Larcker Criteria

# JONATHAN
# correlations between constructs (factors...) should be lower than .7
psi = inspect(SEM_fit, what="std")$psi
psi_fail <- psi
psi_fail[psi_fail<.7] <- NaN
psi_fail

##           DECO  FOOD ATMOS PRODQU CHOICE  PROF BRAND FRENCH AFCOM   SAT    RI
## DECO     1.000                                                               
## FOOD       NaN 1.000                                                         
## ATMOS      NaN   NaN 1.000                                                   
## PRODQUAL   NaN   NaN   NaN  1.000                                            
## CHOICE     NaN   NaN   NaN    NaN  1.000                                     
## PROF       NaN   NaN   NaN    NaN    NaN 1.000                               
## BRAND      NaN   NaN   NaN    NaN    NaN   NaN 1.000                         
## FRENCH     NaN   NaN   NaN    NaN    NaN   NaN   NaN  1.000                  
## AFCOM      NaN   NaN   NaN    NaN    NaN   NaN   NaN    NaN 0.710            
## SAT        NaN   NaN   NaN    NaN    NaN   NaN   NaN    NaN   NaN   NaN      
## RI         NaN   NaN   NaN    NaN    NaN   NaN   NaN    NaN   NaN   NaN   NaN
## COI        NaN   NaN   NaN    NaN    NaN   NaN   NaN    NaN   NaN   NaN   NaN
## Im8        NaN   NaN   NaN    NaN    NaN   NaN   NaN    NaN   NaN   NaN   NaN
## Im15       NaN   NaN   NaN    NaN    NaN   NaN   NaN    NaN   NaN   NaN   NaN
## Im9        NaN   NaN   NaN    NaN    NaN   NaN   NaN    NaN   NaN   NaN   NaN
##            COI   Im8  Im15   Im9
## DECO                            
## FOOD                            
## ATMOS                           
## PRODQUAL                        
## CHOICE                          
## PROF                            
## BRAND                           
## FRENCH                          
## AFCOM                           
## SAT                             
## RI                              
## COI      0.824                  
## Im8        NaN 1.000            
## Im15       NaN   NaN 1.000      
## Im9        NaN   NaN   NaN 1.000

# JONATHAN
# AVE should be higher than squared correlations between constructs

#psi matrix squared
psi2 <- psi^2

# replace diagonal of psi matrix with AVE values
psi2 <- psi2 - psi2 * diag(1,nrow(psi2),ncol(psi2)) + diag(AVE) * diag(1,nrow(AVE),ncol(AVE))

# create matrix with columns filled with AVE
AVE_full <- AVE
AVE_full[is.na(AVE_full)] <- 0 #replace NAs with 0s
AVE_full <- AVE_full^0 %*% AVE_full # multiply a matrix full of ones with AVE_full to get columns filled with AVE

# substract matrices any psi bigger than AVE will be negative
AVEpsi_fail <- AVE_full - psi2
# AVE_full - psi2
AVEpsi_fail[AVEpsi_fail >= 0] <- NaN

AVE_full

##               DECO      FOOD     ATMOS  PRODQUAL    CHOICE      PROF     BRAND
## DECO     0.7986537 0.8840885 0.7042434 0.6266576 0.8801527 0.6600238 0.8358149
## FOOD     0.7986537 0.8840885 0.7042434 0.6266576 0.8801527 0.6600238 0.8358149
## ATMOS    0.7986537 0.8840885 0.7042434 0.6266576 0.8801527 0.6600238 0.8358149
## PRODQUAL 0.7986537 0.8840885 0.7042434 0.6266576 0.8801527 0.6600238 0.8358149
## CHOICE   0.7986537 0.8840885 0.7042434 0.6266576 0.8801527 0.6600238 0.8358149
## PROF     0.7986537 0.8840885 0.7042434 0.6266576 0.8801527 0.6600238 0.8358149
## BRAND    0.7986537 0.8840885 0.7042434 0.6266576 0.8801527 0.6600238 0.8358149
## FRENCH   0.7986537 0.8840885 0.7042434 0.6266576 0.8801527 0.6600238 0.8358149
## AFCOM    0.7986537 0.8840885 0.7042434 0.6266576 0.8801527 0.6600238 0.8358149
## SAT      0.7986537 0.8840885 0.7042434 0.6266576 0.8801527 0.6600238 0.8358149
## RI       0.7986537 0.8840885 0.7042434 0.6266576 0.8801527 0.6600238 0.8358149
## COI      0.7986537 0.8840885 0.7042434 0.6266576 0.8801527 0.6600238 0.8358149
## Im8      0.7986537 0.8840885 0.7042434 0.6266576 0.8801527 0.6600238 0.8358149
## Im15     0.7986537 0.8840885 0.7042434 0.6266576 0.8801527 0.6600238 0.8358149
## Im9      0.7986537 0.8840885 0.7042434 0.6266576 0.8801527 0.6600238 0.8358149
##             FRENCH     AFCOM       SAT        RI       COI Im8 Im15 Im9
## DECO     0.7893477 0.6685779 0.5989777 0.7004635 0.6863754   1    1   1
## FOOD     0.7893477 0.6685779 0.5989777 0.7004635 0.6863754   1    1   1
## ATMOS    0.7893477 0.6685779 0.5989777 0.7004635 0.6863754   1    1   1
## PRODQUAL 0.7893477 0.6685779 0.5989777 0.7004635 0.6863754   1    1   1
## CHOICE   0.7893477 0.6685779 0.5989777 0.7004635 0.6863754   1    1   1
## PROF     0.7893477 0.6685779 0.5989777 0.7004635 0.6863754   1    1   1
## BRAND    0.7893477 0.6685779 0.5989777 0.7004635 0.6863754   1    1   1
## FRENCH   0.7893477 0.6685779 0.5989777 0.7004635 0.6863754   1    1   1
## AFCOM    0.7893477 0.6685779 0.5989777 0.7004635 0.6863754   1    1   1
## SAT      0.7893477 0.6685779 0.5989777 0.7004635 0.6863754   1    1   1
## RI       0.7893477 0.6685779 0.5989777 0.7004635 0.6863754   1    1   1
## COI      0.7893477 0.6685779 0.5989777 0.7004635 0.6863754   1    1   1
## Im8      0.7893477 0.6685779 0.5989777 0.7004635 0.6863754   1    1   1
## Im15     0.7893477 0.6685779 0.5989777 0.7004635 0.6863754   1    1   1
## Im9      0.7893477 0.6685779 0.5989777 0.7004635 0.6863754   1    1   1

psi2

##           DECO  FOOD ATMOS PRODQU CHOICE  PROF BRAND FRENCH AFCOM   SAT    RI
## DECO     0.799                                                               
## FOOD     0.172 0.884                                                         
## ATMOS    0.222 0.089 0.704                                                   
## PRODQUAL 0.222 0.201 0.189  0.627                                            
## CHOICE   0.204 0.085 0.213  0.230  0.880                                     
## PROF     0.438 0.255 0.225  0.293  0.366 0.660                               
## BRAND    0.273 0.106 0.276  0.315  0.266 0.361 0.836                         
## FRENCH   0.113 0.344 0.111  0.098  0.046 0.135 0.101  0.789                  
## AFCOM    0.000 0.000 0.000  0.000  0.000 0.000 0.000  0.000 0.669            
## SAT      0.000 0.000 0.000  0.000  0.000 0.000 0.000  0.000 0.000 0.599      
## RI       0.000 0.000 0.000  0.000  0.000 0.000 0.000  0.000 0.000 0.000 0.700
## COI      0.000 0.000 0.000  0.000  0.000 0.000 0.000  0.000 0.000 0.000 0.001
## Im8      0.000 0.000 0.000  0.000  0.000 0.000 0.000  0.000 0.000 0.000 0.000
## Im15     0.000 0.000 0.000  0.000  0.000 0.000 0.000  0.000 0.000 0.000 0.000
## Im9      0.000 0.000 0.000  0.000  0.000 0.000 0.000  0.000 0.000 0.000 0.000
##            COI   Im8  Im15   Im9
## DECO                            
## FOOD                            
## ATMOS                           
## PRODQUAL                        
## CHOICE                          
## PROF                            
## BRAND                           
## FRENCH                          
## AFCOM                           
## SAT                             
## RI                              
## COI      0.686                  
## Im8      0.000 1.000            
## Im15     0.000 0.117 1.000      
## Im9      0.000 0.195 0.158 1.000

AVEpsi_fail

##            DECO   FOOD  ATMOS PRODQU CHOICE   PROF  BRAND FRENCH  AFCOM    SAT
## DECO          .                                                               
## FOOD        NaN      .                                                        
## ATMOS       NaN    NaN      .                                                 
## PRODQUAL    NaN    NaN    NaN      .                                          
## CHOICE      NaN    NaN    NaN    NaN      .                                   
## PROF        NaN    NaN    NaN    NaN    NaN      .                            
## BRAND       NaN    NaN    NaN    NaN    NaN    NaN      .                     
## FRENCH      NaN    NaN    NaN    NaN    NaN    NaN    NaN      .              
## AFCOM       NaN    NaN    NaN    NaN    NaN    NaN    NaN    NaN      .       
## SAT         NaN    NaN    NaN    NaN    NaN    NaN    NaN    NaN    NaN      .
## RI          NaN    NaN    NaN    NaN    NaN    NaN    NaN    NaN    NaN    NaN
## COI         NaN    NaN    NaN    NaN    NaN    NaN    NaN    NaN    NaN    NaN
## Im8         NaN    NaN    NaN    NaN    NaN    NaN    NaN    NaN    NaN    NaN
## Im15        NaN    NaN    NaN    NaN    NaN    NaN    NaN    NaN    NaN    NaN
## Im9         NaN    NaN    NaN    NaN    NaN    NaN    NaN    NaN    NaN    NaN
##              RI    COI    Im8   Im15    Im9
## DECO                                       
## FOOD                                       
## ATMOS                                      
## PRODQUAL                                   
## CHOICE                                     
## PROF                                       
## BRAND                                      
## FRENCH                                     
## AFCOM                                      
## SAT                                        
## RI            .                            
## COI         NaN      .                     
## Im8         NaN    NaN      .              
## Im15        NaN    NaN    NaN      .       
## Im9         NaN    NaN    NaN    NaN      .

# FERESHTEH
std_fit1=inspect(SEM_fit, "std")
std_fit1$psi^2

##           DECO  FOOD ATMOS PRODQU CHOICE  PROF BRAND FRENCH AFCOM   SAT    RI
## DECO     1.000                                                               
## FOOD     0.172 1.000                                                         
## ATMOS    0.222 0.089 1.000                                                   
## PRODQUAL 0.222 0.201 0.189  1.000                                            
## CHOICE   0.204 0.085 0.213  0.230  1.000                                     
## PROF     0.438 0.255 0.225  0.293  0.366 1.000                               
## BRAND    0.273 0.106 0.276  0.315  0.266 0.361 1.000                         
## FRENCH   0.113 0.344 0.111  0.098  0.046 0.135 0.101  1.000                  
## AFCOM    0.000 0.000 0.000  0.000  0.000 0.000 0.000  0.000 0.504            
## SAT      0.000 0.000 0.000  0.000  0.000 0.000 0.000  0.000 0.000 0.412      
## RI       0.000 0.000 0.000  0.000  0.000 0.000 0.000  0.000 0.000 0.000 0.452
## COI      0.000 0.000 0.000  0.000  0.000 0.000 0.000  0.000 0.000 0.000 0.001
## Im8      0.000 0.000 0.000  0.000  0.000 0.000 0.000  0.000 0.000 0.000 0.000
## Im15     0.000 0.000 0.000  0.000  0.000 0.000 0.000  0.000 0.000 0.000 0.000
## Im9      0.000 0.000 0.000  0.000  0.000 0.000 0.000  0.000 0.000 0.000 0.000
##            COI   Im8  Im15   Im9
## DECO                            
## FOOD                            
## ATMOS                           
## PRODQUAL                        
## CHOICE                          
## PROF                            
## BRAND                           
## FRENCH                          
## AFCOM                           
## SAT                             
## RI                              
## COI      0.679                  
## Im8      0.000 1.000            
## Im15     0.000 0.117 1.000      
## Im9      0.000 0.195 0.158 1.000

2.4.6.3 Modification indices

arrange(modificationindices(SEM_fit),-mi)

##          lhs op      rhs      mi    epc sepc.lv sepc.all sepc.nox
## 1       Im15  ~   CHOICE 183.159  0.499   0.648    0.543    0.543
## 2        Im8  ~     FOOD 165.172  0.650   0.534    0.509    0.509
## 3       Im15  ~     PROF 144.405  0.658   0.611    0.513    0.513
## 4       Im15  ~      SAT 141.622  1.178   0.996    0.836    0.836
## 5        Im8  ~   FRENCH 131.111  0.492   0.480    0.457    0.457
## 6       Im15  ~       RI 126.703  2.198   1.291    1.084    1.084
## 7       Im15  ~    BRAND  87.447  0.374   0.451    0.378    0.378
## 8       Im15  ~ PRODQUAL  85.387  0.649   0.463    0.388    0.388
## 9       Im15  ~    AFCOM  76.869  0.727   0.811    0.681    0.681
## 10      Im15  ~     DECO  69.835  0.321   0.400    0.336    0.336
## 11      Im15  ~    ATMOS  68.865  0.328   0.412    0.346    0.346
## 12      FOOD  ~      Im8  65.017  0.219   0.267    0.280    0.267
## 13    FRENCH  ~      Im8  60.450  0.269   0.276    0.289    0.276
## 14     AFCOM =~   C_REP1  59.740  0.185   0.207    0.284    0.284
## 15    FRENCH  ~    AFCOM  59.527  2.715   3.107    3.107    3.107
## 16      FOOD  ~       RI  52.098  2.996   2.140    2.140    2.140
## 17    C_REP2 ~~   C_REP3  50.550  0.105   0.105    1.324    1.324
## 18    FRENCH  ~      Im9  49.497  0.188   0.193    0.262    0.193
## 19    CHOICE  ~      COI  40.234 -3.741  -4.851   -4.851   -4.851
## 20    CHOICE  ~     Im15  39.667  0.240   0.185    0.221    0.185
## 21      Im16 ~~     Im19  34.438  4.282   4.282    9.391    9.391
## 22       SAT  ~       RI  34.427  1.296   0.901    0.901    0.901
## 23       SAT  ~    AFCOM  34.426  0.240   0.317    0.317    0.317
## 24     AFCOM ~~      SAT  34.426  0.213   0.334    0.334    0.334
## 25     AFCOM  ~      SAT  34.426  0.463   0.351    0.351    0.351
## 26     AFCOM  ~       RI  34.426  2.423   1.275    1.275    1.275
## 27     AFCOM  ~      COI  34.423 -1.282  -1.932   -1.932   -1.932
## 28       Im1 ~~      Im2  34.420 18.676  18.676  114.920  114.920
## 29       SAT  ~      COI  34.420  0.446   0.888    0.888    0.888
## 30       Im6 ~~      Im7  34.413 20.484  20.484   86.144   86.144
## 31       Im9  ~    BRAND  31.665  0.245   0.295    0.217    0.217
## 32      FOOD  ~    AFCOM  31.388  1.549   2.103    2.103    2.103
## 33       Im9  ~   FRENCH  31.242  0.304   0.296    0.218    0.218
## 34    COM_A1 ~~   COM_A2  29.695  0.282   0.282    0.368    0.368
## 35       Im8  ~      SAT  28.978  0.459   0.388    0.370    0.370
## 36       Im9  ~ PRODQUAL  27.649  0.402   0.287    0.211    0.211
## 37      Im15  ~      COI  26.365  0.636   1.069    0.897    0.897
## 38       Im8  ~    AFCOM  23.181  0.343   0.383    0.365    0.365
## 39    CHOICE  ~      SAT  21.757  2.413   1.573    1.573    1.573
## 40     ATMOS =~   C_REP1  21.130  0.092   0.116    0.159    0.159
## 41     BRAND =~     Im13  18.982  0.196   0.235    0.196    0.196
## 42    FRENCH  ~      SAT  17.983  1.753   1.520    1.520    1.520
## 43      Im11 ~~     Im13  17.611 -0.175  -0.175   -0.313   -0.313
## 44      PROF  ~     Im15  17.562  0.114   0.122    0.146    0.122
## 45        RI =~    SAT_2  16.582  0.270   0.159    0.161    0.161
## 46       Im9  ~       RI  16.466  0.863   0.507    0.373    0.373
## 47      PROF  ~      COI  16.252 -1.692  -3.063   -3.063   -3.063
## 48       Im8  ~     PROF  16.089  0.189   0.176    0.167    0.167
## 49  PRODQUAL  ~      Im9  15.723  0.078   0.109    0.148    0.109
## 50     AFCOM =~   C_REP2  15.496 -0.080  -0.090   -0.145   -0.145
## 51    CHOICE =~     Im20  14.579 -0.153  -0.199   -0.134   -0.134
## 52     BRAND =~     Im12  14.319 -0.161  -0.194   -0.172   -0.172
## 53      Im21 ~~     Im22  13.959 -0.240  -0.240   -0.397   -0.397
## 54    C_REP1 ~~   C_REP3  13.821 -0.050  -0.050   -0.325   -0.325
## 55       Im9  ~      COI  13.779  0.501   0.842    0.619    0.619
## 56       Im8  ~       RI  13.567  0.619   0.364    0.347    0.347
## 57        RI =~     Im22  13.510 -0.319  -0.188   -0.123   -0.123
## 58      PROF  ~      SAT  13.460  1.351   1.229    1.229    1.229
## 59     BRAND  ~       RI  13.269 -2.130  -1.040   -1.040   -1.040
## 60      FOOD =~     Im11  12.957  0.218   0.180    0.156    0.156
## 61    COM_A3 ~~   C_REP1  12.934  0.079   0.079    0.197    0.197
## 62     AFCOM =~   C_REP3  12.654 -0.069  -0.077   -0.138   -0.138
## 63    CHOICE =~     Im13  12.494  0.128   0.167    0.138    0.138
## 64       Im9  ~    ATMOS  12.301  0.151   0.190    0.139    0.139
## 65  PRODQUAL  ~      COI  12.163 -1.204  -2.843   -2.843   -2.843
## 66       SAT =~   COM_A3  12.153  0.218   0.184    0.116    0.116
## 67      Im21 ~~   C_REP3  11.927  0.055   0.055    0.181    0.181
## 68     AFCOM =~     Im11  11.658  0.139   0.155    0.135    0.135
## 69       SAT =~    C_CR4  11.299  0.268   0.227    0.113    0.113
## 70      Im11 ~~     Im12  11.197  0.133   0.133    0.265    0.265
## 71     BRAND  ~      Im9  11.157  0.099   0.082    0.112    0.082
## 72       Im9  ~    AFCOM  11.029  0.300   0.335    0.246    0.246
## 73     AFCOM =~    SAT_2  10.908  0.102   0.114    0.115    0.115
## 74    C_REP1 ~~   C_REP2  10.704 -0.074  -0.074   -0.777   -0.777
## 75       Im8  ~     DECO  10.609  0.108   0.134    0.128    0.128
## 76      Im13 ~~      Im1  10.426  0.068   0.068    0.379    0.379
## 77     ATMOS =~     Im12  10.359 -0.114  -0.143   -0.127   -0.127
## 78       Im8  ~      COI  10.225 -0.341  -0.573   -0.546   -0.546
## 79    CHOICE =~   C_REP1  10.161  0.056   0.073    0.100    0.100
## 80  PRODQUAL  ~     Im15  10.071  0.071   0.099    0.118    0.099
## 81    CHOICE =~     Im12   9.645 -0.107  -0.139   -0.123   -0.123
## 82    COM_A1 ~~   COM_A4   9.547 -0.174  -0.174   -0.216   -0.216
## 83  PRODQUAL =~    C_CR4   9.541  0.288   0.205    0.103    0.103
## 84        RI =~     Im21   9.488  0.256   0.150    0.110    0.110
## 85    COM_A3 ~~   COM_A4   9.441  0.197   0.197    0.228    0.228
## 86     BRAND =~     Im20   9.439 -0.143  -0.172   -0.116   -0.116
## 87       SAT =~   C_REP1   9.272  0.094   0.080    0.109    0.109
## 88     ATMOS =~   C_REP3   9.231 -0.049  -0.062   -0.112   -0.112
## 89      Im13 ~~     Im17   9.200  0.068   0.068    0.354    0.354
## 90    CHOICE =~   C_REP3   9.155 -0.043  -0.056   -0.102   -0.102
## 91     ATMOS =~    C_CR4   9.000  0.162   0.203    0.101    0.101
## 92     BRAND =~     Im22   8.810  0.142   0.171    0.112    0.112
## 93      Im10 ~~      Im6   8.547 -0.042  -0.042   -0.177   -0.177
## 94       COI =~    SAT_2   8.312  0.059   0.099    0.101    0.101
## 95       Im1 ~~    SAT_2   8.278 -0.054  -0.054   -0.323   -0.323
## 96       Im4 ~~     Im17   8.269 -0.044  -0.044   -0.412   -0.412
## 97      PROF =~   COM_A3   8.050  0.170   0.158    0.099    0.099
## 98       COI =~   C_REP1   7.976  0.038   0.064    0.088    0.088
## 99    FRENCH =~   C_REP1   7.877  0.065   0.063    0.087    0.087
## 100     Im19 ~~   C_REP1   7.751 -0.044  -0.044   -0.174   -0.174
## 101 PRODQUAL =~    C_CR1   7.682 -0.249  -0.177   -0.090   -0.090
## 102       RI =~   COM_A1   7.525  0.245   0.144    0.102    0.102
## 103     FOOD  ~      SAT   7.485  0.889   0.914    0.914    0.914
## 104     FOOD =~      Im6   7.424 -0.326  -0.268   -0.222   -0.222
## 105     FOOD =~      Im7   7.423  0.388   0.319    0.264    0.264
## 106     Im22 ~~   C_REP3   7.422 -0.043  -0.043   -0.168   -0.168
## 107     DECO =~   COM_A3   7.297  0.110   0.137    0.086    0.086
## 108     DECO =~     Im20   7.257 -0.113  -0.141   -0.095   -0.095
## 109 PRODQUAL  ~      SAT   7.194  0.812   0.964    0.964    0.964
## 110   COM_A4 ~~    SAT_1   7.082  0.084   0.084    0.176    0.176
## 111     Im10 ~~      Im7   7.054  0.039   0.039    0.349    0.349
## 112   COM_A2 ~~   COM_A3   7.034 -0.155  -0.155   -0.190   -0.190
## 113     DECO =~    C_CR1   6.848 -0.128  -0.160   -0.081   -0.081
## 114     DECO =~     Im22   6.804  0.112   0.140    0.092    0.092
## 115      Im9  ~     DECO   6.773  0.109   0.136    0.100    0.100
## 116      SAT =~   COM_A2   6.750 -0.156  -0.132   -0.084   -0.084
## 117 PRODQUAL  ~       RI   6.743 -1.005  -0.829   -0.829   -0.829
## 118     DECO =~   C_REP1   6.732  0.047   0.059    0.081    0.081
## 119     PROF =~   COM_A2   6.708 -0.149  -0.139   -0.088   -0.088
## 120     Im10 ~~     Im16   6.670  0.042   0.042    0.163    0.163
## 121    ATMOS =~     Im11   6.644  0.105   0.132    0.115    0.115
## 122    BRAND =~   COM_A3   6.498  0.109   0.131    0.083    0.083
## 123      Im3 ~~      Im1   6.455 -0.037  -0.037   -0.290   -0.290
## 124    BRAND =~      Im7   6.442 -0.103  -0.124   -0.102   -0.102
## 125    BRAND =~      Im6   6.442  0.086   0.104    0.086    0.086
## 126   FRENCH =~     Im22   6.178  0.126   0.123    0.080    0.080
## 127    BRAND =~      Im4   6.147 -0.068  -0.082   -0.061   -0.061
## 128     PROF =~   C_REP3   6.141 -0.054  -0.051   -0.091   -0.091
## 129    BRAND =~    C_CR4   6.121  0.131   0.158    0.079    0.079
## 130     PROF =~    C_CR4   5.926  0.175   0.163    0.081    0.081
## 131 PRODQUAL =~      Im5   5.859  0.168   0.120    0.091    0.091
## 132      Im9  ~      SAT   5.824  0.260   0.220    0.162    0.162
## 133     DECO =~    C_CR4   5.804  0.122   0.153    0.076    0.076
## 134   CHOICE =~      Im5   5.770  0.085   0.111    0.084    0.084
## 135     Im10 ~~     Im13   5.689 -0.034  -0.034   -0.163   -0.163
## 136    ATMOS =~   COM_A1   5.661 -0.104  -0.131   -0.093   -0.093
## 137   FRENCH =~     Im20   5.467 -0.116  -0.113   -0.076   -0.076
## 138    SAT_2 ~~    SAT_3   5.461 -0.090  -0.090   -0.182   -0.182
## 139      SAT =~     Im13   5.450  0.121   0.102    0.085    0.085
## 140     Im20 ~~     Im21   5.394  0.135   0.135    0.200    0.200
## 141     DECO =~      Im7   5.391 -0.092  -0.115   -0.095   -0.095
## 142     DECO =~      Im6   5.391  0.077   0.097    0.080    0.080
## 143     DECO =~   C_REP3   5.381 -0.034  -0.043   -0.077   -0.077
## 144     Im20 ~~     Im17   5.374 -0.062  -0.062   -0.252   -0.252
## 145       RI =~     Im14   5.347  0.083   0.049    0.057    0.057
## 146      SAT =~     Im12   5.344 -0.113  -0.096   -0.085   -0.085
## 147     Im22 ~~      Im1   5.277  0.058   0.058    0.281    0.281
## 148      SAT =~   C_REP2   5.268 -0.060  -0.050   -0.081   -0.081
## 149    BRAND =~      Im5   5.219  0.093   0.112    0.085    0.085
## 150     Im10 ~~   COM_A2   5.199  0.042   0.042    0.144    0.144
## 151     FOOD =~   COM_A3   5.174  0.140   0.115    0.072    0.072
## 152 PRODQUAL =~      Im2   5.160 -0.140  -0.100   -0.078   -0.078
## 153 PRODQUAL =~      Im1   5.160  0.158   0.113    0.085    0.085
## 154     Im13 ~~      Im2   5.135 -0.047  -0.047   -0.137   -0.137
## 155     PROF =~    SAT_2   5.119  0.122   0.113    0.115    0.115
## 156    ATMOS =~      Im5   5.108  0.088   0.111    0.084    0.084
## 157     FOOD =~   C_REP1   5.098  0.062   0.051    0.070    0.070
## 158     DECO =~   COM_A2   4.936 -0.087  -0.109   -0.069   -0.069
## 159     Im22 ~~   C_REP1   4.912  0.042   0.042    0.138    0.138
## 160     FOOD =~     Im13   4.890 -0.123  -0.101   -0.084   -0.084
## 161     Im15  ~     FOOD   4.877  0.130   0.107    0.090    0.090
## 162      SAT =~    C_CR1   4.841 -0.169  -0.143   -0.072   -0.072
## 163   COM_A1 ~~    SAT_3   4.827  0.086   0.086    0.117    0.117
## 164     Im20 ~~      Im6   4.779 -0.068  -0.068   -0.122   -0.122
## 165     Im22 ~~    SAT_3   4.772 -0.081  -0.081   -0.136   -0.136
## 166     DECO =~     Im18   4.758  0.096   0.120    0.086    0.086
## 167     DECO =~     Im17   4.757 -0.097  -0.121   -0.097   -0.097
## 168      Im3 ~~   COM_A4   4.750  0.056   0.056    0.136    0.136
## 169     Im13 ~~     Im16   4.740 -0.065  -0.065   -0.137   -0.137
## 170     PROF  ~       RI   4.713  1.021   0.646    0.646    0.646
## 171   FRENCH =~   C_REP2   4.709 -0.041  -0.040   -0.065   -0.065
## 172   COM_A3 ~~   C_REP2   4.694 -0.036  -0.036   -0.173   -0.173
## 173       RI =~     Im12   4.683 -0.143  -0.084   -0.074   -0.074
## 174   CHOICE =~     Im22   4.682  0.089   0.115    0.075    0.075
## 175 PRODQUAL  ~    AFCOM   4.643  0.556   0.871    0.871    0.871
## 176    BRAND =~   C_REP3   4.640 -0.034  -0.041   -0.073   -0.073
## 177   C_REP2 ~~    C_CR4   4.622 -0.046  -0.046   -0.174   -0.174
## 178    SAT_1 ~~    SAT_3   4.621  0.088   0.088    0.203    0.203
## 179    SAT_3 ~~    C_CR3   4.566 -0.121  -0.121   -0.122   -0.122
## 180       RI =~   COM_A2   4.550 -0.203  -0.119   -0.076   -0.076
## 181     PROF =~     Im12   4.548 -0.125  -0.116   -0.103   -0.103
## 182     Im14 ~~     Im16   4.540 -0.034  -0.034   -0.167   -0.167
## 183      Im4 ~~   COM_A3   4.513  0.052   0.052    0.164    0.164
## 184      Im4 ~~     Im18   4.475  0.039   0.039    0.158    0.158
## 185     Im11 ~~      Im6   4.442 -0.067  -0.067   -0.105   -0.105
## 186     Im11 ~~      Im1   4.439 -0.054  -0.054   -0.205   -0.205
## 187    AFCOM =~      Im5   4.429  0.083   0.092    0.070    0.070
## 188      Im9  ~     FOOD   4.393  0.134   0.110    0.081    0.081
## 189    BRAND =~    C_CR1   4.276 -0.106  -0.127   -0.064   -0.064
## 190     Im22 ~~   C_REP2   4.263 -0.030  -0.030   -0.189   -0.189
## 191   FRENCH =~    C_CR4   4.258  0.136   0.133    0.066    0.066
## 192      Im3 ~~      Im5   4.251 -0.068  -0.068   -0.176   -0.176
## 193    ATMOS =~      Im4   4.243 -0.053  -0.066   -0.049   -0.049
## 194     Im22 ~~     Im11   4.210  0.078   0.078    0.122    0.122
## 195     Im20 ~~     Im13   4.208  0.064   0.064    0.131    0.131
## 196      Im3 ~~      Im4   4.172  0.149   0.149    0.976    0.976
## 197   FRENCH  ~       RI   4.156  1.077   0.649    0.649    0.649
## 198       RI =~      Im5   4.112  0.150   0.088    0.067    0.067
## 199     Im19 ~~   C_REP2   4.098  0.025   0.025    0.191    0.191
## 200     Im14 ~~      Im6   4.077  0.028   0.028    0.154    0.154
## 201     FOOD =~    C_CR4   4.070  0.156   0.129    0.064    0.064
## 202    BRAND =~    SAT_2   3.969  0.063   0.076    0.077    0.077
## 203      Im4 ~~    C_CR1   3.952 -0.060  -0.060   -0.169   -0.169
## 204     PROF =~    SAT_1   3.880 -0.110  -0.102   -0.103   -0.103
## 205     Im12 ~~    SAT_3   3.872  0.057   0.057    0.122    0.122
## 206     Im20 ~~   COM_A4   3.870  0.087   0.087    0.118    0.118
## 207      Im5 ~~      Im6   3.867 -0.060  -0.060   -0.098   -0.098
## 208     PROF =~     Im20   3.855 -0.122  -0.113   -0.076   -0.076
## 209      Im1 ~~   C_REP3   3.796 -0.020  -0.020   -0.196   -0.196
## 210    AFCOM =~      Im1   3.790 -0.065  -0.072   -0.055   -0.055
## 211     PROF =~    C_CR1   3.790 -0.135  -0.125   -0.063   -0.063
## 212      Im9  ~     PROF   3.775  0.116   0.108    0.079    0.079
## 213      Im4 ~~      Im6   3.774  0.035   0.035    0.143    0.143
## 214      Im3 ~~      Im2   3.769  0.029   0.029    0.116    0.116
## 215     Im11 ~~   C_REP1   3.758  0.038   0.038    0.098    0.098
## 216 PRODQUAL =~   C_REP3   3.731 -0.053  -0.038   -0.069   -0.069
## 217    SAT_1 ~~   C_REP2   3.720 -0.020  -0.020   -0.180   -0.180
## 218     Im12 ~~      Im7   3.683  0.045   0.045    0.239    0.239
## 219      Im4 ~~     Im11   3.680 -0.042  -0.042   -0.136   -0.136
## 220     Im13 ~~    SAT_2   3.635  0.044   0.044    0.123    0.123
## 221       RI =~    SAT_1   3.625 -0.128  -0.075   -0.076   -0.076
## 222     FOOD =~      Im5   3.621  0.105   0.087    0.066    0.066
## 223   FRENCH =~   COM_A3   3.610  0.102   0.099    0.062    0.062
## 224    ATMOS =~   COM_A4   3.553  0.094   0.119    0.069    0.069
## 225      Im1 ~~    SAT_1   3.461  0.034   0.034    0.232    0.232
## 226   COM_A4 ~~   C_REP1   3.446  0.042   0.042    0.104    0.104
## 227     PROF =~   C_REP1   3.436  0.050   0.047    0.064    0.064
## 228      SAT =~   COM_A4   3.433  0.119   0.101    0.059    0.059
## 229     Im14 ~~      Im7   3.426 -0.027  -0.027   -0.308   -0.308
## 230   COM_A1 ~~   COM_A3   3.382 -0.096  -0.096   -0.119   -0.119
## 231      Im8  ~    ATMOS   3.351  0.062   0.078    0.075    0.075
## 232     Im10 ~~    C_CR1   3.323  0.043   0.043    0.125    0.125
## 233      Im2 ~~    SAT_2   3.300  0.034   0.034    0.105    0.105
## 234     Im22 ~~    SAT_2   3.284 -0.050  -0.050   -0.122   -0.122
## 235     Im20 ~~    SAT_1   3.261 -0.049  -0.049   -0.121   -0.121
## 236    AFCOM =~     Im20   3.256 -0.090  -0.101   -0.068   -0.068
## 237      Im8  ~ PRODQUAL   3.250  0.109   0.078    0.074    0.074
## 238      Im3 ~~     Im17   3.234  0.028   0.028    0.201    0.201
## 239      COI =~      Im1   3.223 -0.036  -0.060   -0.045   -0.045
## 240     PROF  ~    AFCOM   3.217  0.562   0.675    0.675    0.675
## 241   CHOICE =~     Im19   3.207 -0.096  -0.124   -0.109   -0.109
## 242   CHOICE =~     Im16   3.207  0.092   0.119    0.098    0.098
## 243    AFCOM =~     Im12   3.185 -0.060  -0.067   -0.059   -0.059
## 244     Im11 ~~     Im17   3.178 -0.048  -0.048   -0.170   -0.170
## 245    SAT_2 ~~   C_REP1   3.171  0.026   0.026    0.102    0.102
## 246     Im13 ~~   C_REP2   3.161  0.021   0.021    0.156    0.156
## 247    AFCOM =~     Im16   3.149 -0.078  -0.087   -0.072   -0.072
## 248      COI =~   C_REP2   3.131 -0.020  -0.033   -0.054   -0.054
## 249     Im20 ~~   C_REP2   3.127  0.026   0.026    0.146    0.146
## 250       RI =~     Im10   3.125 -0.063  -0.037   -0.042   -0.042
## 251   COM_A1 ~~    SAT_1   3.111 -0.049  -0.049   -0.111   -0.111
## 252     Im17 ~~   C_REP1   3.109 -0.024  -0.024   -0.177   -0.177
## 253      SAT =~      Im5   3.082  0.095   0.081    0.061    0.061
## 254      Im5 ~~      Im1   3.070  0.043   0.043    0.171    0.171
## 255   CHOICE =~     Im21   3.060  0.068   0.088    0.064    0.064
## 256     Im14 ~~    C_CR1   3.026 -0.040  -0.040   -0.147   -0.147
## 257     Im22 ~~   COM_A1   2.999 -0.067  -0.067   -0.109   -0.109
## 258   COM_A3 ~~   C_REP3   2.992 -0.031  -0.031   -0.093   -0.093
## 259      Im2 ~~     Im16   2.917  0.042   0.042    0.096    0.096
## 260    AFCOM =~    C_CR4   2.915  0.109   0.122    0.061    0.061
## 261    BRAND  ~      COI   2.911 -0.890  -1.243   -1.243   -1.243
## 262     Im14 ~~    SAT_2   2.905  0.021   0.021    0.137    0.137
## 263      Im5 ~~   COM_A2   2.867  0.068   0.068    0.089    0.089
## 264     PROF =~      Im2   2.845  0.134   0.124    0.097    0.097
## 265     PROF =~      Im1   2.845 -0.151  -0.140   -0.105   -0.105
## 266     Im22 ~~    SAT_1   2.817  0.045   0.045    0.125    0.125
## 267      Im2 ~~     Im17   2.808  0.030   0.030    0.170    0.170
## 268    ATMOS =~    C_CR1   2.804 -0.087  -0.109   -0.055   -0.055
## 269     Im13 ~~   COM_A2   2.796 -0.057  -0.057   -0.105   -0.105
## 270      Im5 ~~   C_REP1   2.796  0.031   0.031    0.085    0.085
## 271 PRODQUAL =~    SAT_2   2.792  0.090   0.064    0.065    0.065
## 272 PRODQUAL =~      Im4   2.789 -0.077  -0.055   -0.041   -0.041
## 273     FOOD =~    C_CR1   2.775 -0.124  -0.102   -0.052   -0.052
## 274 PRODQUAL =~    SAT_1   2.773 -0.092  -0.065   -0.066   -0.066
## 275     Im10 ~~     Im12   2.738  0.022   0.022    0.118    0.118
## 276   FRENCH =~     Im19   2.732  0.089   0.087    0.077    0.077
## 277   FRENCH =~     Im16   2.732 -0.085  -0.083   -0.069   -0.069
## 278     Im12 ~~      Im6   2.722 -0.039  -0.039   -0.101   -0.101
## 279     Im18 ~~   COM_A1   2.714 -0.055  -0.055   -0.088   -0.088
## 280     Im18 ~~      Im6   2.708  0.044   0.044    0.086    0.086
## 281   FRENCH =~     Im11   2.704  0.079   0.077    0.067    0.067
## 282     Im11 ~~    SAT_1   2.699  0.045   0.045    0.098    0.098
## 283     Im20 ~~     Im22   2.655  0.132   0.132    0.235    0.235
## 284     PROF =~     Im13   2.648  0.101   0.093    0.078    0.078
## 285    ATMOS =~   C_REP2   2.633 -0.027  -0.034   -0.056   -0.056
## 286     Im16 ~~   C_REP3   2.610 -0.025  -0.025   -0.088   -0.088
## 287    ATMOS =~     Im13   2.605  0.060   0.076    0.063    0.063
## 288      Im3 ~~     Im11   2.557  0.036   0.036    0.090    0.090
## 289   COM_A1 ~~   C_REP2   2.557  0.024   0.024    0.125    0.125
## 290     FOOD =~   C_REP2   2.543 -0.036  -0.030   -0.048   -0.048
## 291   COM_A4 ~~    C_CR4   2.538  0.104   0.104    0.094    0.094
## 292      COI =~     Im11   2.487  0.042   0.071    0.062    0.062
## 293     DECO =~     Im12   2.478 -0.056  -0.070   -0.062   -0.062
## 294     Im11 ~~   C_REP2   2.476 -0.023  -0.023   -0.115   -0.115
## 295      COI =~     Im13   2.474 -0.036  -0.061   -0.051   -0.051
## 296     Im14 ~~   COM_A2   2.462 -0.028  -0.028   -0.122   -0.122
## 297      Im7 ~~   COM_A1   2.454 -0.048  -0.048   -0.165   -0.165
## 298      Im2 ~~    C_CR1   2.446  0.055   0.055    0.095    0.095
## 299     Im22 ~~     Im13   2.413 -0.048  -0.048   -0.110   -0.110
## 300     Im13 ~~   C_REP1   2.404 -0.025  -0.025   -0.093   -0.093
## 301     Im14 ~~     Im12   2.400 -0.020  -0.020   -0.137   -0.137
## 302      SAT =~     Im17   2.389  0.084   0.071    0.057    0.057
## 303     Im21 ~~    C_CR4   2.381  0.087   0.087    0.086    0.086
## 304      Im2 ~~   C_REP2   2.380 -0.015  -0.015   -0.120   -0.120
## 305      SAT =~     Im20   2.366 -0.092  -0.078   -0.052   -0.052
## 306      Im3 ~~   COM_A3   2.344 -0.039  -0.039   -0.093   -0.093
## 307     Im10 ~~     Im11   2.330  0.026   0.026    0.088    0.088
## 308   FRENCH =~   COM_A2   2.329 -0.079  -0.077   -0.049   -0.049
## 309     Im22 ~~     Im12   2.328 -0.044  -0.044   -0.113   -0.113
## 310      Im7 ~~   C_REP2   2.326 -0.018  -0.018   -0.237   -0.237
## 311   CHOICE =~    C_CR4   2.319  0.074   0.096    0.048    0.048
## 312   CHOICE =~   COM_A3   2.319  0.061   0.079    0.049    0.049
## 313    SAT_2 ~~    C_CR3   2.317  0.064   0.064    0.094    0.094
## 314      COI =~     Im16   2.311 -0.041  -0.070   -0.058   -0.058
## 315    SAT_1 ~~    C_CR4   2.293  0.061   0.061    0.100    0.100
## 316      Im4 ~~      Im1   2.293  0.022   0.022    0.220    0.220
## 317      Im1 ~~     Im17   2.268 -0.028  -0.028   -0.306   -0.306
## 318     Im14 ~~     Im20   2.265 -0.025  -0.025   -0.119   -0.119
## 319   FRENCH =~    C_CR1   2.260 -0.095  -0.093   -0.047   -0.047
## 320   FRENCH =~   COM_A1   2.237 -0.073  -0.071   -0.050   -0.050
## 321      Im3 ~~     Im22   2.231  0.033   0.033    0.104    0.104
## 322     Im16 ~~    SAT_1   2.225 -0.040  -0.040   -0.100   -0.100
## 323   C_REP3 ~~    C_CR3   2.221 -0.035  -0.035   -0.084   -0.084
## 324     Im19 ~~   COM_A1   2.217  0.048   0.048    0.094    0.094
## 325     Im21 ~~    C_CR3   2.214 -0.085  -0.085   -0.085   -0.085
## 326    AFCOM =~      Im2   2.212  0.044   0.049    0.039    0.039
## 327   COM_A2 ~~    SAT_2   2.179 -0.045  -0.045   -0.088   -0.088
## 328   COM_A1 ~~    C_CR3   2.166  0.086   0.086    0.085    0.085
## 329    ATMOS =~   COM_A3   2.159  0.071   0.089    0.056    0.056
## 330     FOOD =~    SAT_1   2.120 -0.068  -0.056   -0.056   -0.056
## 331      COI =~      Im2   2.097  0.025   0.043    0.033    0.033
## 332     Im20 ~~     Im19   2.061  0.045   0.045    0.097    0.097
## 333       RI =~     Im16   2.057 -0.120  -0.071   -0.059   -0.059
## 334     Im18 ~~   C_REP1   2.030  0.024   0.024    0.076    0.076
## 335     FOOD =~     Im20   2.029 -0.082  -0.067   -0.045   -0.045
## 336      Im2 ~~   C_REP1   2.027  0.018   0.018    0.076    0.076
## 337       RI =~     Im11   2.008  0.113   0.066    0.057    0.057
## 338     Im11 ~~      Im2   1.971  0.036   0.036    0.071    0.071
## 339      SAT =~     Im18   1.959 -0.076  -0.065   -0.046   -0.046
## 340 PRODQUAL =~   C_REP2   1.957  0.040   0.028    0.046    0.046
## 341     Im14 ~~   COM_A3   1.954  0.026   0.026    0.107    0.107
## 342     Im14 ~~   C_REP3   1.939  0.010   0.010    0.102    0.102
## 343     FOOD  ~      COI   1.922  0.513   1.050    1.050    1.050
## 344    SAT_1 ~~    C_CR1   1.895 -0.052  -0.052   -0.099   -0.099
## 345   COM_A3 ~~    SAT_1   1.886  0.042   0.042    0.089    0.089
## 346      Im4 ~~   COM_A4   1.882 -0.035  -0.035   -0.108   -0.108
## 347     Im20 ~~      Im1   1.878 -0.035  -0.035   -0.151   -0.151
## 348    ATMOS  ~     Im15   1.869  0.055   0.044    0.052    0.044
## 349    ATMOS  ~      COI   1.869 -0.851  -1.140   -1.140   -1.140
## 350     Im10 ~~    SAT_2   1.865 -0.017  -0.017   -0.089   -0.089
## 351     PROF =~     Im22   1.856  0.087   0.081    0.053    0.053
## 352   COM_A2 ~~    SAT_3   1.854  0.056   0.056    0.075    0.075
## 353     Im12 ~~     Im16   1.844  0.038   0.038    0.089    0.089
## 354      SAT =~     Im11   1.825  0.078   0.066    0.058    0.058
## 355 PRODQUAL =~     Im17   1.814  0.122   0.087    0.070    0.070
## 356 PRODQUAL =~     Im18   1.813 -0.122  -0.087   -0.062   -0.062
## 357    BRAND =~      Im3   1.795  0.036   0.043    0.033    0.033
## 358   CHOICE =~     Im14   1.792  0.022   0.029    0.033    0.033
## 359   CHOICE =~     Im10   1.792 -0.022  -0.029   -0.032   -0.032
## 360     Im20 ~~   COM_A1   1.791 -0.053  -0.053   -0.076   -0.076
## 361      Im5 ~~     Im16   1.790 -0.047  -0.047   -0.070   -0.070
## 362      Im1 ~~   COM_A4   1.789 -0.039  -0.039   -0.145   -0.145
## 363      Im5 ~~    SAT_2   1.783  0.036   0.036    0.073    0.073
## 364     Im17 ~~   COM_A1   1.777  0.037   0.037    0.135    0.135
## 365      SAT =~   COM_A1   1.771  0.076   0.064    0.045    0.045
## 366      SAT =~     Im14   1.764  0.038   0.032    0.038    0.038
## 367     Im13 ~~    SAT_3   1.744 -0.041  -0.041   -0.079   -0.079
## 368    ATMOS  ~      SAT   1.741  0.720   0.485    0.485    0.485
## 369     Im12 ~~   COM_A2   1.738  0.042   0.042    0.086    0.086
## 370      Im2 ~~    SAT_1   1.737 -0.024  -0.024   -0.084   -0.084
## 371   COM_A4 ~~    SAT_3   1.721 -0.057  -0.057   -0.073   -0.073
## 372    BRAND  ~     Im15   1.708  0.044   0.037    0.044    0.037
## 373    AFCOM =~     Im21   1.704  0.063   0.070    0.051    0.051
## 374    BRAND =~    SAT_1   1.671 -0.042  -0.050   -0.051   -0.051
## 375     Im10 ~~     Im20   1.670  0.022   0.022    0.083    0.083
## 376      Im7 ~~   COM_A2   1.645 -0.041  -0.041   -0.140   -0.140
## 377   COM_A3 ~~    SAT_2   1.644  0.041   0.041    0.075    0.075
## 378      Im4 ~~      Im2   1.644 -0.019  -0.019   -0.097   -0.097
## 379     Im22 ~~     Im19   1.630 -0.040  -0.040   -0.096   -0.096
## 380     Im13 ~~     Im18   1.625 -0.034  -0.034   -0.077   -0.077
## 381   CHOICE  ~    AFCOM   1.617  0.560   0.482    0.482    0.482
## 382    AFCOM =~      Im6   1.610  0.046   0.052    0.043    0.043
## 383    BRAND =~   C_REP1   1.582  0.024   0.029    0.040    0.040
## 384 PRODQUAL =~      Im6   1.581 -0.076  -0.054   -0.045   -0.045
## 385 PRODQUAL =~      Im7   1.581  0.091   0.065    0.053    0.053
## 386     Im14 ~~      Im2   1.548  0.014   0.014    0.093    0.093
## 387   C_REP3 ~~    C_CR4   1.542  0.029   0.029    0.068    0.068
## 388     Im22 ~~      Im2   1.521 -0.031  -0.031   -0.078   -0.078
## 389   FRENCH  ~     Im15   1.520  0.038   0.039    0.046    0.039
## 390    BRAND =~   COM_A2   1.499 -0.050  -0.061   -0.039   -0.039
## 391     Im21 ~~     Im18   1.498 -0.040  -0.040   -0.065   -0.065
## 392   COM_A1 ~~    SAT_2   1.478  0.035   0.035    0.070    0.070
## 393      Im2 ~~   C_REP3   1.458  0.013   0.013    0.064    0.064
## 394 PRODQUAL =~     Im16   1.429 -0.108  -0.077   -0.063   -0.063
## 395 PRODQUAL =~     Im19   1.428  0.112   0.080    0.071    0.071
## 396   FRENCH =~      Im2   1.418  0.037   0.036    0.028    0.028
## 397   FRENCH =~      Im1   1.418 -0.042  -0.041   -0.031   -0.031
## 398       RI =~     Im13   1.418  0.083   0.049    0.041    0.041
## 399      Im3 ~~     Im18   1.405 -0.022  -0.022   -0.070   -0.070
## 400     FOOD =~      Im2   1.404  0.046   0.038    0.030    0.030
## 401     FOOD =~      Im1   1.404 -0.052  -0.043   -0.032   -0.032
## 402      Im1 ~~   C_REP2   1.400  0.012   0.012    0.179    0.179
## 403      Im2 ~~     Im18   1.397 -0.026  -0.026   -0.063   -0.063
## 404     DECO =~     Im13   1.375  0.044   0.055    0.045    0.045
## 405    ATMOS =~   COM_A2   1.373 -0.055  -0.069   -0.044   -0.044
## 406      Im3 ~~    C_CR1   1.368  0.036   0.036    0.079    0.079
## 407      Im5 ~~      Im7   1.361  0.033   0.033    0.115    0.115
## 408     Im12 ~~   COM_A4   1.347 -0.039  -0.039   -0.077   -0.077
## 409 PRODQUAL =~   COM_A2   1.343 -0.082  -0.058   -0.037   -0.037
## 410     Im19 ~~    SAT_2   1.338  0.028   0.028    0.080    0.080
## 411    ATMOS =~     Im18   1.327  0.053   0.067    0.048    0.048
## 412    ATMOS =~     Im17   1.326 -0.053  -0.067   -0.054   -0.054
## 413   COM_A1 ~~   C_REP3   1.314  0.019   0.019    0.061    0.061
## 414   COM_A1 ~~    C_CR1   1.313 -0.063  -0.063   -0.070   -0.070
## 415   C_REP1 ~~    C_CR3   1.298  0.033   0.033    0.065    0.065
## 416     Im16 ~~    C_CR4   1.296 -0.061  -0.061   -0.066   -0.066
## 417      Im4 ~~    C_CR3   1.278  0.037   0.037    0.091    0.091
## 418    ATMOS =~    C_CR3   1.273 -0.062  -0.078   -0.037   -0.037
## 419     Im20 ~~    SAT_2   1.270  0.032   0.032    0.069    0.069
## 420     Im10 ~~   C_REP3   1.270 -0.008  -0.008   -0.067   -0.067
## 421     Im19 ~~      Im7   1.262  0.030   0.030    0.149    0.149
## 422     Im14 ~~     Im13   1.262  0.015   0.015    0.095    0.095
## 423     Im19 ~~   COM_A2   1.251 -0.038  -0.038   -0.073   -0.073
## 424     Im12 ~~    C_CR1   1.237 -0.045  -0.045   -0.079   -0.079
## 425     Im12 ~~     Im13   1.229  0.080   0.080    0.235    0.235
## 426     Im20 ~~   COM_A2   1.221 -0.046  -0.046   -0.065   -0.065
## 427      SAT =~     Im10   1.220 -0.032  -0.027   -0.030   -0.030
## 428   COM_A4 ~~   C_REP3   1.218 -0.020  -0.020   -0.061   -0.061
## 429     Im12 ~~     Im17   1.213 -0.023  -0.023   -0.135   -0.135
## 430      Im6 ~~   C_REP2   1.208  0.013   0.013    0.083    0.083
## 431     Im18 ~~   C_REP3   1.193 -0.015  -0.015   -0.057   -0.057
## 432     PROF  ~      Im8   1.179  0.033   0.036    0.038    0.036
## 433     Im11 ~~   COM_A3   1.178  0.048   0.048    0.056    0.056
## 434    BRAND =~   COM_A4   1.173 -0.048  -0.058   -0.034   -0.034
## 435      Im5 ~~     Im14   1.168  0.017   0.017    0.076    0.076
## 436     Im21 ~~    SAT_3   1.162  0.041   0.041    0.057    0.057
## 437      SAT =~     Im21   1.157  0.063   0.053    0.039    0.039
## 438    BRAND  ~      Im8   1.141 -0.041  -0.034   -0.036   -0.034
## 439      Im6 ~~   COM_A1   1.138  0.035   0.035    0.056    0.056
## 440   CHOICE =~   COM_A4   1.134 -0.044  -0.057   -0.033   -0.033
## 441      Im1 ~~   COM_A3   1.130 -0.030  -0.030   -0.112   -0.112
## 442    AFCOM =~    C_CR1   1.115 -0.065  -0.073   -0.037   -0.037
## 443     Im13 ~~    C_CR3   1.113 -0.049  -0.049   -0.068   -0.068
## 444 PRODQUAL =~   COM_A3   1.105  0.077   0.055    0.034    0.034
## 445     PROF =~      Im7   1.105 -0.065  -0.061   -0.050   -0.050
## 446     PROF =~      Im6   1.105  0.055   0.051    0.042    0.042
## 447     Im14 ~~     Im17   1.101  0.012   0.012    0.150    0.150
## 448      Im5 ~~      Im2   1.096 -0.026  -0.026   -0.053   -0.053
## 449      Im7 ~~    SAT_3   1.096  0.031   0.031    0.108    0.108
## 450      Im3 ~~     Im12   1.095 -0.018  -0.018   -0.072   -0.072
## 451   FRENCH =~   COM_A4   1.093  0.058   0.056    0.033    0.033
## 452     Im12 ~~    C_CR3   1.088  0.045   0.045    0.070    0.070
## 453   COM_A4 ~~    C_CR3   1.088 -0.069  -0.069   -0.063   -0.063
## 454   COM_A2 ~~    C_CR1   1.080  0.060   0.060    0.066    0.066
## 455     FOOD =~    SAT_2   1.076  0.047   0.039    0.039    0.039
## 456     Im12 ~~   COM_A3   1.075 -0.034  -0.034   -0.067   -0.067
## 457     Im17 ~~   COM_A4   1.070 -0.032  -0.032   -0.110   -0.110
## 458     Im21 ~~     Im11   1.069 -0.040  -0.040   -0.052   -0.052
## 459      SAT =~      Im4   1.057 -0.036  -0.030   -0.022   -0.022
## 460      Im7 ~~   COM_A4   1.041  0.035   0.035    0.113    0.113
## 461     Im12 ~~    SAT_1   1.034 -0.021  -0.021   -0.076   -0.076
## 462     Im13 ~~   COM_A4   1.025  0.037   0.037    0.064    0.064
## 463     Im16 ~~    C_CR1   1.018  0.051   0.051    0.064    0.064
## 464    ATMOS  ~    AFCOM   1.017  0.469   0.417    0.417    0.417
## 465      Im7 ~~   C_REP3   1.017  0.012   0.012    0.103    0.103
## 466      Im1 ~~     Im18   1.014  0.022   0.022    0.104    0.104
## 467      Im2 ~~   COM_A3   1.013  0.029   0.029    0.055    0.055
## 468     Im11 ~~      Im7   1.007  0.030   0.030    0.099    0.099
## 469   COM_A1 ~~   C_REP1   1.001 -0.020  -0.020   -0.054   -0.054
## 470     Im13 ~~      Im7   0.983 -0.025  -0.025   -0.118   -0.118
## 471     PROF =~      Im4   0.981 -0.049  -0.045   -0.033   -0.033
## 472     Im20 ~~    SAT_3   0.979  0.037   0.037    0.056    0.056
## 473      Im3 ~~   COM_A2   0.978 -0.024  -0.024   -0.061   -0.061
## 474     Im22 ~~     Im18   0.976  0.032   0.032    0.062    0.062
## 475     Im10 ~~     Im17   0.963 -0.012  -0.012   -0.112   -0.112
## 476     Im19 ~~    SAT_3   0.943 -0.030  -0.030   -0.061   -0.061
## 477     Im12 ~~   C_REP1   0.938 -0.014  -0.014   -0.060   -0.060
## 478    ATMOS =~      Im2   0.931 -0.032  -0.040   -0.032   -0.032
## 479    ATMOS =~      Im1   0.931  0.036   0.046    0.034    0.034
## 480     Im18 ~~   COM_A2   0.927  0.034   0.034    0.053    0.053
## 481      SAT =~      Im2   0.925  0.047   0.039    0.031    0.031
## 482      COI =~      Im5   0.921  0.024   0.041    0.031    0.031
## 483     DECO =~    SAT_2   0.918  0.028   0.035    0.035    0.035
## 484   FRENCH =~      Im5   0.917  0.043   0.042    0.032    0.032
## 485     Im18 ~~    SAT_1   0.917 -0.022  -0.022   -0.060   -0.060
## 486     Im18 ~~      Im7   0.913 -0.024  -0.024   -0.099   -0.099
## 487      COI =~      Im4   0.910 -0.015  -0.025   -0.019   -0.019
## 488    ATMOS =~      Im3   0.904  0.024   0.030    0.023    0.023
## 489      Im3 ~~    SAT_1   0.901  0.015   0.015    0.066    0.066
## 490   COM_A2 ~~   COM_A4   0.899 -0.061  -0.061   -0.074   -0.074
## 491   FRENCH =~     Im13   0.895 -0.040  -0.039   -0.032   -0.032
## 492      Im6 ~~    SAT_1   0.893  0.021   0.021    0.058    0.058
## 493     Im14 ~~     Im21   0.885  0.015   0.015    0.070    0.070
## 494   FRENCH  ~      COI   0.875 -0.441  -0.760   -0.760   -0.760
## 495      Im5 ~~     Im19   0.866 -0.028  -0.028   -0.055   -0.055
## 496   CHOICE =~   COM_A2   0.866 -0.036  -0.046   -0.029   -0.029
## 497       RI =~      Im7   0.865 -0.071  -0.042   -0.034   -0.034
## 498      Im4 ~~     Im22   0.864 -0.020  -0.020   -0.082   -0.082
## 499     Im19 ~~     Im17   0.855  0.022   0.022    0.119    0.119
## 500      SAT =~    C_CR3   0.854 -0.075  -0.064   -0.030   -0.030
## 501     Im12 ~~    SAT_2   0.853 -0.020  -0.020   -0.062   -0.062
## 502      Im4 ~~      Im7   0.849 -0.016  -0.016   -0.136   -0.136
## 503   COM_A4 ~~    SAT_2   0.847  0.030   0.030    0.055    0.055
## 504     Im10 ~~   COM_A3   0.844 -0.018  -0.018   -0.057   -0.057
## 505   COM_A2 ~~    C_CR3   0.840 -0.056  -0.056   -0.055   -0.055
## 506    SAT_3 ~~   C_REP3   0.838  0.015   0.015    0.048    0.048
## 507     Im16 ~~   COM_A4   0.837 -0.039  -0.039   -0.054   -0.054
## 508    SAT_3 ~~    C_CR1   0.834  0.048   0.048    0.055    0.055
## 509     Im13 ~~      Im6   0.826  0.023   0.023    0.053    0.053
## 510     Im22 ~~    C_CR1   0.824 -0.048  -0.048   -0.065   -0.065
## 511     Im20 ~~     Im18   0.824  0.030   0.030    0.052    0.052
## 512     Im22 ~~     Im17   0.821  0.024   0.024    0.110    0.110
## 513       RI =~      Im6   0.819  0.058   0.034    0.028    0.028
## 514    BRAND =~    SAT_3   0.814 -0.035  -0.042   -0.038   -0.038
## 515     PROF =~     Im17   0.812  0.077   0.072    0.058    0.058
## 516     PROF =~     Im18   0.812 -0.077  -0.072   -0.051   -0.051
## 517     PROF =~      Im5   0.810  0.061   0.056    0.043    0.043
## 518     Im17 ~~      Im7   0.808 -0.020  -0.020   -0.188   -0.188
## 519      Im9  ~   CHOICE   0.808  0.036   0.047    0.034    0.034
## 520       RI =~      Im4   0.805 -0.042  -0.024   -0.018   -0.018
## 521     Im12 ~~    C_CR4   0.796  0.038   0.038    0.058    0.058
## 522   COM_A3 ~~    SAT_3   0.787 -0.038  -0.038   -0.048   -0.048
## 523     Im13 ~~     Im19   0.786  0.023   0.023    0.064    0.064
## 524      Im4 ~~      Im5   0.780  0.031   0.031    0.104    0.104
## 525     Im11 ~~   COM_A2   0.780  0.037   0.037    0.047    0.047
## 526     Im10 ~~   COM_A4   0.779 -0.017  -0.017   -0.056   -0.056
## 527      Im1 ~~   COM_A1   0.777  0.023   0.023    0.091    0.091
## 528     Im11 ~~     Im18   0.776  0.029   0.029    0.045    0.045
## 529     Im11 ~~    C_CR4   0.772  0.050   0.050    0.047    0.047
## 530     Im12 ~~      Im2   0.767 -0.017  -0.017   -0.055   -0.055
## 531    AFCOM =~    SAT_1   0.759  0.026   0.029    0.030    0.030
## 532   CHOICE =~    C_CR1   0.757 -0.041  -0.053   -0.027   -0.027
## 533      Im7 ~~    SAT_2   0.750 -0.019  -0.019   -0.099   -0.099
## 534    BRAND =~     Im10   0.744 -0.016  -0.019   -0.022   -0.022
## 535    BRAND =~     Im14   0.744  0.016   0.019    0.023    0.023
## 536     Im22 ~~      Im6   0.743  0.027   0.027    0.053    0.053
## 537    AFCOM =~      Im7   0.743 -0.037  -0.042   -0.034   -0.034
## 538     Im16 ~~   COM_A1   0.742 -0.032  -0.032   -0.048   -0.048
## 539     FOOD =~     Im22   0.740  0.050   0.041    0.027    0.027
## 540      SAT =~     Im22   0.737 -0.052  -0.044   -0.029   -0.029
## 541      COI =~    SAT_3   0.737 -0.023  -0.038   -0.035   -0.035
## 542      Im7 ~~    C_CR4   0.735  0.038   0.038    0.094    0.094
## 543     FOOD =~   COM_A2   0.734 -0.051  -0.042   -0.026   -0.026
## 544     Im17 ~~   C_REP2   0.731  0.009   0.009    0.128    0.128
## 545     FOOD  ~      Im9   0.726  0.018   0.022    0.030    0.022
## 546      Im5 ~~     Im22   0.725  0.031   0.031    0.051    0.051
## 547     Im10 ~~   COM_A1   0.724 -0.015  -0.015   -0.052   -0.052
## 548     Im10 ~~    C_CR4   0.719 -0.021  -0.021   -0.054   -0.054
## 549     Im22 ~~   COM_A3   0.719  0.036   0.036    0.055    0.055
## 550     Im17 ~~   C_REP3   0.716  0.009   0.009    0.083    0.083
## 551     Im16 ~~    SAT_3   0.714  0.031   0.031    0.047    0.047
## 552   FRENCH =~    SAT_3   0.713  0.040   0.039    0.035    0.035
## 553    AFCOM =~     Im14   0.709  0.016   0.018    0.021    0.021
## 554      Im5 ~~     Im11   0.707  0.032   0.032    0.040    0.040
## 555      COI =~   COM_A1   0.689 -0.025  -0.041   -0.029   -0.029
## 556     Im19 ~~   C_REP3   0.683  0.011   0.011    0.051    0.051
## 557      Im5 ~~   C_REP2   0.682 -0.012  -0.012   -0.060   -0.060
## 558     Im22 ~~      Im7   0.676  0.025   0.025    0.103    0.103
## 559    BRAND =~     Im11   0.674 -0.038  -0.045   -0.039   -0.039
## 560     Im14 ~~    SAT_1   0.668 -0.010  -0.010   -0.073   -0.073
## 561      Im6 ~~    C_CR4   0.665 -0.038  -0.038   -0.045   -0.045
## 562     Im10 ~~    C_CR3   0.664 -0.021  -0.021   -0.053   -0.053
## 563     FOOD =~   COM_A1   0.662 -0.045  -0.037   -0.026   -0.026
## 564      SAT =~      Im1   0.662 -0.044  -0.037   -0.028   -0.028
## 565     Im22 ~~     Im16   0.660  0.029   0.029    0.053    0.053
## 566     Im14 ~~    C_CR4   0.657  0.020   0.020    0.063    0.063
## 567      COI =~   C_REP3   0.654 -0.009  -0.015   -0.027   -0.027
## 568     Im21 ~~   COM_A4   0.652 -0.036  -0.036   -0.045   -0.045
## 569      Im4 ~~     Im16   0.652  0.017   0.017    0.064    0.064
## 570   CHOICE  ~       RI   0.646  0.531   0.241    0.241    0.241
## 571    SAT_3 ~~   C_REP2   0.632 -0.011  -0.011   -0.061   -0.061
## 572    ATMOS  ~      Im9   0.632  0.028   0.022    0.030    0.022
## 573   C_REP2 ~~    C_CR3   0.627  0.017   0.017    0.066    0.066
## 574    BRAND =~     Im16   0.626 -0.044  -0.053   -0.044   -0.044
## 575    BRAND =~     Im19   0.626  0.046   0.055    0.049    0.049
## 576     Im17 ~~   COM_A3   0.626  0.024   0.024    0.082    0.082
## 577     Im21 ~~   C_REP1   0.616 -0.015  -0.015   -0.042   -0.042
## 578      Im4 ~~     Im12   0.614  0.013   0.013    0.069    0.069
## 579     Im20 ~~   COM_A3   0.607 -0.034  -0.034   -0.045   -0.045
## 580      Im7 ~~   COM_A3   0.604  0.026   0.026    0.084    0.084
## 581     Im14 ~~     Im18   0.601 -0.011  -0.011   -0.058   -0.058
## 582      Im5 ~~    C_CR4   0.601  0.042   0.042    0.041    0.041
## 583     Im14 ~~    C_CR3   0.598  0.019   0.019    0.062    0.062
## 584    ATMOS =~    SAT_2   0.591  0.023   0.029    0.030    0.030
## 585     Im16 ~~      Im7   0.590 -0.022  -0.022   -0.085   -0.085
## 586     Im13 ~~   COM_A1   0.582  0.025   0.025    0.046    0.046
## 587     PROF =~     Im11   0.582  0.048   0.045    0.039    0.039
## 588     Im19 ~~     Im18   0.579 -0.020  -0.020   -0.048   -0.048
## 589       RI =~     Im19   0.577  0.066   0.039    0.034    0.034
## 590     Im16 ~~   COM_A3   0.574  0.031   0.031    0.043    0.043
## 591      Im4 ~~   C_REP3   0.567 -0.007  -0.007   -0.055   -0.055
## 592    SAT_1 ~~    C_CR3   0.565 -0.031  -0.031   -0.051   -0.051
## 593     Im11 ~~   COM_A1   0.557 -0.030  -0.030   -0.038   -0.038
## 594     Im11 ~~    SAT_2   0.547 -0.021  -0.021   -0.040   -0.040
## 595     FOOD =~      Im4   0.540 -0.026  -0.022   -0.016   -0.016
## 596       RI =~     Im18   0.533 -0.051  -0.030   -0.021   -0.021
## 597    BRAND  ~      SAT   0.532  0.334   0.234    0.234    0.234
## 598     Im20 ~~   C_REP3   0.528 -0.012  -0.012   -0.041   -0.041
## 599      Im1 ~~    C_CR1   0.525 -0.026  -0.026   -0.085   -0.085
## 600   COM_A4 ~~   C_REP2   0.524 -0.012  -0.012   -0.059   -0.059
## 601 PRODQUAL =~     Im22   0.522 -0.056  -0.040   -0.026   -0.026
## 602      Im2 ~~      Im7   0.520  0.014   0.014    0.075    0.075
## 603       RI =~      Im1   0.520 -0.044  -0.026   -0.020   -0.020
## 604     Im22 ~~   COM_A4   0.516  0.031   0.031    0.048    0.048
## 605      Im1 ~~   COM_A2   0.512  0.020   0.020    0.077    0.077
## 606      Im6 ~~   COM_A3   0.509 -0.025  -0.025   -0.038   -0.038
## 607     Im17 ~~    SAT_2   0.503  0.014   0.014    0.078    0.078
## 608     DECO  ~      SAT   0.503  0.339   0.230    0.230    0.230
## 609     Im17 ~~      Im6   0.499  0.015   0.015    0.070    0.070
## 610      Im2 ~~   COM_A1   0.490 -0.018  -0.018   -0.038   -0.038
## 611      Im6 ~~    SAT_3   0.489 -0.022  -0.022   -0.036   -0.036
## 612      COI =~   COM_A3   0.489 -0.023  -0.038   -0.024   -0.024
## 613   C_REP3 ~~    C_CR1   0.487  0.015   0.015    0.042    0.042
## 614      Im3 ~~     Im20   0.485 -0.016  -0.016   -0.044   -0.044
## 615     Im22 ~~   COM_A2   0.481  0.028   0.028    0.045    0.045
## 616     DECO  ~     Im15   0.479  0.024   0.020    0.023    0.020
## 617   COM_A2 ~~    SAT_1   0.479 -0.020  -0.020   -0.045   -0.045
## 618     Im21 ~~    SAT_2   0.473 -0.019  -0.019   -0.039   -0.039
## 619     Im10 ~~     Im18   0.472  0.010   0.010    0.041    0.041
## 620      SAT =~      Im7   0.469 -0.041  -0.034   -0.028   -0.028
## 621     Im19 ~~   COM_A3   0.467 -0.024  -0.024   -0.044   -0.044
## 622     DECO  ~      COI   0.466 -0.373  -0.502   -0.502   -0.502
## 623     Im21 ~~     Im17   0.465  0.018   0.018    0.069    0.069
## 624       RI =~     Im20   0.464  0.058   0.034    0.023    0.023
## 625   CHOICE =~      Im3   0.462 -0.016  -0.020   -0.015   -0.015
## 626      Im3 ~~     Im19   0.454  0.013   0.013    0.048    0.048
## 627     Im17 ~~    SAT_3   0.448 -0.018  -0.018   -0.067   -0.067
## 628     Im20 ~~      Im7   0.446  0.020   0.020    0.075    0.075
## 629    AFCOM =~     Im10   0.444 -0.013  -0.014   -0.016   -0.016
## 630     Im20 ~~      Im2   0.443 -0.017  -0.017   -0.038   -0.038
## 631   COM_A2 ~~   C_REP2   0.441 -0.010  -0.010   -0.054   -0.054
## 632     FOOD =~    SAT_3   0.441  0.038   0.031    0.028    0.028
## 633     Im10 ~~    SAT_3   0.435  0.011   0.011    0.040    0.040
## 634      Im2 ~~     Im19   0.432 -0.014  -0.014   -0.042   -0.042
## 635    AFCOM =~    SAT_3   0.431  0.026   0.030    0.027    0.027
## 636     Im21 ~~   COM_A1   0.430  0.026   0.026    0.035    0.035
## 637     Im13 ~~   COM_A3   0.428 -0.023  -0.023   -0.040   -0.040
## 638     PROF =~   COM_A4   0.422 -0.040  -0.037   -0.022   -0.022
## 639   COM_A1 ~~    C_CR4   0.421 -0.038  -0.038   -0.036   -0.036
## 640     Im10 ~~      Im2   0.421 -0.007  -0.007   -0.039   -0.039
## 641     DECO =~     Im11   0.415  0.026   0.032    0.028    0.028
## 642      Im3 ~~      Im7   0.411 -0.011  -0.011   -0.074   -0.074
## 643      Im6 ~~   COM_A2   0.411  0.022   0.022    0.035    0.035
## 644   CHOICE =~   COM_A1   0.407  0.023   0.030    0.021    0.021
## 645   CHOICE =~     Im11   0.402 -0.025  -0.032   -0.028   -0.028
## 646 PRODQUAL =~   COM_A1   0.400  0.042   0.030    0.021    0.021
## 647   COM_A2 ~~    C_CR4   0.384 -0.038  -0.038   -0.036   -0.036
## 648      COI =~     Im21   0.382  0.017   0.029    0.021    0.021
## 649     PROF =~   COM_A1   0.381  0.034   0.031    0.022    0.022
## 650     Im17 ~~    C_CR1   0.380 -0.023  -0.023   -0.071   -0.071
## 651    BRAND  ~    AFCOM   0.379  0.240   0.222    0.222    0.222
## 652      Im5 ~~     Im21   0.379 -0.023  -0.023   -0.031   -0.031
## 653      COI =~      Im3   0.370  0.009   0.016    0.012    0.012
## 654    ATMOS =~     Im10   0.367 -0.011  -0.014   -0.016   -0.016
## 655    ATMOS =~     Im14   0.367  0.011   0.014    0.016    0.016
## 656     PROF =~     Im21   0.364  0.036   0.033    0.024    0.024
## 657      COI =~     Im22   0.363 -0.017  -0.029   -0.019   -0.019
## 658     Im12 ~~   COM_A1   0.362  0.018   0.018    0.038    0.038
## 659    BRAND =~      Im2   0.361  0.023   0.028    0.022    0.022
## 660    BRAND =~      Im1   0.361 -0.026  -0.032   -0.024   -0.024
## 661      SAT =~      Im6   0.360  0.030   0.025    0.021    0.021
## 662 PRODQUAL =~     Im20   0.354  0.045   0.032    0.022    0.022
## 663      Im5 ~~    C_CR3   0.350 -0.033  -0.033   -0.032   -0.032
## 664     FOOD =~     Im21   0.347  0.033   0.027    0.020    0.020
## 665     Im16 ~~   C_REP1   0.347  0.011   0.011    0.033    0.033
## 666     Im11 ~~   COM_A4   0.344  0.026   0.026    0.031    0.031
## 667   CHOICE  ~      Im8   0.342 -0.025  -0.020   -0.020   -0.020
## 668    ATMOS  ~      Im8   0.337  0.027   0.021    0.022    0.021
## 669     DECO  ~    AFCOM   0.336  0.236   0.211    0.211    0.211
## 670     Im16 ~~    C_CR3   0.332 -0.031  -0.031   -0.035   -0.035
## 671      COI =~    SAT_1   0.332 -0.012  -0.020   -0.020   -0.020
## 672     DECO =~    SAT_3   0.326 -0.021  -0.026   -0.023   -0.023
## 673     Im10 ~~     Im22   0.323 -0.010  -0.010   -0.040   -0.040
## 674      Im5 ~~   COM_A4   0.307 -0.024  -0.024   -0.030   -0.030
## 675     Im20 ~~    C_CR1   0.306  0.029   0.029    0.036    0.036
## 676     FOOD =~   COM_A4   0.305 -0.035  -0.029   -0.017   -0.017
## 677      Im6 ~~   C_REP3   0.304 -0.007  -0.007   -0.028   -0.028
## 678    BRAND =~   C_REP2   0.302  0.009   0.011    0.017    0.017
## 679   CHOICE =~    C_CR3   0.301 -0.027  -0.035   -0.017   -0.017
## 680      Im7 ~~    SAT_1   0.299 -0.012  -0.012   -0.069   -0.069
## 681     Im12 ~~   C_REP2   0.297  0.006   0.006    0.050    0.050
## 682     FOOD  ~     Im15   0.296 -0.013  -0.016   -0.019   -0.016
## 683   CHOICE =~      Im4   0.295 -0.013  -0.016   -0.012   -0.012
## 684    AFCOM =~    C_CR3   0.294 -0.035  -0.040   -0.019   -0.019
## 685     Im21 ~~      Im2   0.292  0.014   0.014    0.029    0.029
## 686     Im14 ~~   C_REP1   0.292  0.004   0.004    0.040    0.040
## 687      Im5 ~~   COM_A1   0.290 -0.021  -0.021   -0.027   -0.027
## 688    ATMOS =~    SAT_3   0.290 -0.020  -0.026   -0.023   -0.023
## 689      Im5 ~~     Im17   0.281  0.014   0.014    0.050    0.050
## 690       RI =~      Im2   0.280  0.029   0.017    0.013    0.013
## 691     DECO =~    SAT_1   0.280 -0.016  -0.020   -0.020   -0.020
## 692       RI =~    C_CR1   0.280 -0.057  -0.033   -0.017   -0.017
## 693   FRENCH =~      Im3   0.280 -0.015  -0.015   -0.011   -0.011
## 694      COI =~   COM_A4   0.279  0.018   0.030    0.018    0.018
## 695   COM_A3 ~~    C_CR3   0.276  0.034   0.034    0.031    0.031
## 696     FOOD =~     Im19   0.274  0.038   0.031    0.027    0.027
## 697     FOOD =~     Im16   0.274 -0.036  -0.030   -0.025   -0.025
## 698     Im21 ~~   COM_A2   0.273  0.022   0.022    0.029    0.029
## 699     Im10 ~~     Im19   0.271 -0.007  -0.007   -0.038   -0.038
## 700     Im21 ~~      Im1   0.271  0.013   0.013    0.054    0.054
## 701   CHOICE =~     Im17   0.271  0.022   0.028    0.023    0.023
## 702   CHOICE =~     Im18   0.271 -0.022  -0.028   -0.020   -0.020
## 703     DECO =~   COM_A1   0.264 -0.019  -0.024   -0.017   -0.017
## 704      Im3 ~~    SAT_2   0.260 -0.008  -0.008   -0.032   -0.032
## 705      Im8  ~   CHOICE   0.259 -0.016  -0.021   -0.020   -0.020
## 706    AFCOM =~     Im19   0.258 -0.023  -0.025   -0.022   -0.022
## 707      Im1 ~~    SAT_3   0.257  0.013   0.013    0.052    0.052
## 708     Im16 ~~    SAT_2   0.253  0.014   0.014    0.030    0.030
## 709      Im2 ~~   COM_A4   0.253  0.015   0.015    0.028    0.028
## 710     PROF =~      Im3   0.251  0.024   0.022    0.017    0.017
## 711      COI =~     Im19   0.250  0.014   0.024    0.021    0.021
## 712     Im12 ~~   C_REP3   0.250 -0.006  -0.006   -0.031   -0.031
## 713     Im17 ~~   COM_A2   0.246 -0.014  -0.014   -0.052   -0.052
## 714     Im14 ~~     Im11   0.243  0.008   0.008    0.035    0.035
## 715     Im19 ~~    SAT_1   0.242 -0.012  -0.012   -0.038   -0.038
## 716     Im14 ~~     Im22   0.240  0.008   0.008    0.043    0.043
## 717    AFCOM =~     Im22   0.237  0.025   0.028    0.018    0.018
## 718   COM_A2 ~~   C_REP3   0.237 -0.008  -0.008   -0.027   -0.027
## 719      Im6 ~~    C_CR1   0.237  0.021   0.021    0.029    0.029
## 720     Im10 ~~     Im21   0.236 -0.008  -0.008   -0.029   -0.029
## 721     Im14 ~~   C_REP2   0.234 -0.003  -0.003   -0.053   -0.053
## 722    SAT_2 ~~    C_CR1   0.233 -0.019  -0.019   -0.031   -0.031
## 723      Im1 ~~      Im6   0.232 -0.010  -0.010   -0.049   -0.049
## 724      Im7 ~~    C_CR1   0.226 -0.020  -0.020   -0.057   -0.057
## 725   CHOICE =~    SAT_2   0.223 -0.015  -0.019   -0.019   -0.019
## 726    AFCOM =~      Im4   0.222 -0.012  -0.013   -0.010   -0.010
## 727      Im7 ~~   C_REP1   0.218  0.007   0.007    0.048    0.048
## 728     Im21 ~~    C_CR1   0.217  0.025   0.025    0.028    0.028
## 729      Im5 ~~    SAT_1   0.212 -0.012  -0.012   -0.027   -0.027
## 730     DECO =~   C_REP2   0.212 -0.007  -0.009   -0.014   -0.014
## 731 PRODQUAL =~      Im3   0.210  0.021   0.015    0.011    0.011
## 732 PRODQUAL =~     Im10   0.207 -0.017  -0.012   -0.014   -0.014
## 733 PRODQUAL =~     Im14   0.207  0.017   0.012    0.014    0.014
## 734     Im21 ~~      Im7   0.206 -0.014  -0.014   -0.047   -0.047
## 735       RI =~   COM_A4   0.201  0.046   0.027    0.016    0.016
## 736     Im21 ~~     Im16   0.200 -0.016  -0.016   -0.025   -0.025
## 737     Im20 ~~   C_REP1   0.197 -0.009  -0.009   -0.025   -0.025
## 738      COI =~     Im12   0.194  0.010   0.016    0.014    0.014
## 739    SAT_1 ~~   C_REP1   0.192  0.006   0.006    0.028    0.028
## 740      Im5 ~~    SAT_3   0.192 -0.016  -0.016   -0.022   -0.022
## 741      Im4 ~~   COM_A2   0.192 -0.010  -0.010   -0.034   -0.034
## 742      Im2 ~~    C_CR4   0.191 -0.016  -0.016   -0.025   -0.025
## 743   CHOICE =~   C_REP2   0.187 -0.006  -0.008   -0.013   -0.013
## 744     Im14 ~~    SAT_3   0.183 -0.007  -0.007   -0.032   -0.032
## 745     Im18 ~~   C_REP2   0.179 -0.005  -0.005   -0.033   -0.033
## 746     Im18 ~~    C_CR1   0.177  0.019   0.019    0.025    0.025
## 747   COM_A3 ~~    C_CR1   0.177 -0.025  -0.025   -0.026   -0.026
## 748     Im11 ~~    C_CR1   0.175 -0.023  -0.023   -0.024   -0.024
## 749     Im14 ~~      Im1   0.172 -0.005  -0.005   -0.060   -0.060
## 750     FOOD =~   C_REP3   0.171 -0.009  -0.008   -0.014   -0.014
## 751    SAT_2 ~~    C_CR4   0.170  0.017   0.017    0.025    0.025
## 752     DECO =~      Im2   0.170  0.013   0.016    0.013    0.013
## 753     DECO =~      Im1   0.170 -0.015  -0.018   -0.014   -0.014
## 754     DECO =~    C_CR3   0.167  0.021   0.026    0.013    0.013
## 755   FRENCH =~    C_CR3   0.167 -0.027  -0.027   -0.013   -0.013
## 756      SAT =~   C_REP3   0.165 -0.010  -0.009   -0.015   -0.015
## 757     Im17 ~~    C_CR4   0.163  0.016   0.016    0.043    0.043
## 758 PRODQUAL =~   COM_A4   0.162 -0.030  -0.022   -0.013   -0.013
## 759     DECO  ~      Im8   0.161  0.016   0.013    0.014    0.013
## 760      Im3 ~~   C_REP3   0.159  0.004   0.004    0.023    0.023
## 761     Im15  ~   FRENCH   0.157  0.020   0.019    0.016    0.016
## 762     Im17 ~~    SAT_1   0.155  0.008   0.008    0.048    0.048
## 763      Im4 ~~   COM_A1   0.152  0.009   0.009    0.029    0.029
## 764     Im16 ~~     Im18   0.152 -0.012  -0.012   -0.022   -0.022
## 765   FRENCH =~     Im18   0.151  0.016   0.016    0.011    0.011
## 766   FRENCH =~     Im17   0.151 -0.016  -0.016   -0.013   -0.013
## 767     DECO  ~      Im9   0.150  0.012   0.010    0.013    0.010
## 768    AFCOM =~     Im18   0.148 -0.014  -0.016   -0.011   -0.011
## 769      Im3 ~~   COM_A1   0.148 -0.009  -0.009   -0.023   -0.023
## 770      Im3 ~~   C_REP2   0.146 -0.003  -0.003   -0.033   -0.033
## 771      Im3 ~~    C_CR3   0.138 -0.012  -0.012   -0.024   -0.024
## 772     Im22 ~~    C_CR3   0.137  0.021   0.021    0.025    0.025
## 773    ATMOS =~    SAT_1   0.136 -0.011  -0.014   -0.014   -0.014
## 774    C_CR1 ~~    C_CR3   0.135  0.101   0.101    0.083    0.083
## 775     Im19 ~~   COM_A4   0.135 -0.013  -0.013   -0.024   -0.024
## 776     PROF  ~      Im9   0.133 -0.009  -0.009   -0.013   -0.009
## 777      Im1 ~~     Im16   0.132 -0.009  -0.009   -0.040   -0.040
## 778       RI =~   COM_A3   0.125  0.035   0.020    0.013    0.013
## 779      Im4 ~~   C_REP2   0.124  0.003   0.003    0.038    0.038
## 780      Im2 ~~   COM_A2   0.123 -0.010  -0.010   -0.020   -0.020
## 781     Im17 ~~    C_CR3   0.122  0.014   0.014    0.038    0.038
## 782     Im11 ~~     Im16   0.121 -0.013  -0.013   -0.018   -0.018
## 783   C_REP2 ~~    C_CR1   0.118  0.007   0.007    0.030    0.030
## 784      Im3 ~~    SAT_3   0.115 -0.008  -0.008   -0.020   -0.020
## 785      Im1 ~~    C_CR3   0.115 -0.013  -0.013   -0.038   -0.038
## 786    AFCOM =~     Im17   0.115  0.013   0.014    0.011    0.011
## 787      Im4 ~~     Im14   0.115 -0.003  -0.003   -0.036   -0.036
## 788     Im19 ~~    C_CR3   0.114  0.016   0.016    0.023    0.023
## 789    ATMOS =~     Im19   0.113  0.016   0.020    0.018    0.018
## 790    ATMOS =~     Im16   0.113 -0.015  -0.019   -0.016   -0.016
## 791    SAT_3 ~~    C_CR4   0.113  0.019   0.019    0.019    0.019
## 792      Im4 ~~    C_CR4   0.111  0.011   0.011    0.026    0.026
## 793   FRENCH =~     Im21   0.110 -0.016  -0.016   -0.011   -0.011
## 794     Im10 ~~    SAT_1   0.110  0.004   0.004    0.024    0.024
## 795      Im3 ~~    C_CR4   0.109 -0.011  -0.011   -0.020   -0.020
## 796       RI =~    C_CR4   0.103  0.036   0.021    0.010    0.010
## 797     Im20 ~~     Im11   0.103  0.012   0.012    0.017    0.017
## 798   CHOICE =~    SAT_1   0.102  0.010   0.013    0.013    0.013
## 799      Im4 ~~    SAT_2   0.101 -0.005  -0.005   -0.026   -0.026
## 800     Im21 ~~     Im12   0.101  0.009   0.009    0.020    0.020
## 801     PROF =~    SAT_3   0.100 -0.020  -0.019   -0.017   -0.017
## 802   CHOICE =~      Im7   0.100  0.011   0.014    0.012    0.012
## 803   CHOICE =~      Im6   0.100 -0.009  -0.012   -0.010   -0.010
## 804     Im14 ~~   COM_A1   0.099  0.005   0.005    0.024    0.024
## 805     PROF =~    C_CR3   0.093 -0.022  -0.021   -0.010   -0.010
## 806   FRENCH =~    SAT_2   0.092 -0.011  -0.011   -0.011   -0.011
## 807      Im4 ~~    SAT_1   0.092 -0.005  -0.005   -0.027   -0.027
## 808    SAT_2 ~~   C_REP3   0.090  0.004   0.004    0.017    0.017
## 809      Im5 ~~     Im12   0.089  0.008   0.008    0.018    0.018
## 810     PROF =~   C_REP2   0.087  0.007   0.006    0.010    0.010
## 811      Im6 ~~    SAT_2   0.087 -0.007  -0.007   -0.017   -0.017
## 812       RI =~    SAT_3   0.085 -0.024  -0.014   -0.013   -0.013
## 813      Im2 ~~      Im6   0.083 -0.006  -0.006   -0.015   -0.015
## 814     Im18 ~~    C_CR3   0.082 -0.014  -0.014   -0.016   -0.016
## 815   FRENCH =~    SAT_1   0.081 -0.011  -0.011   -0.011   -0.011
## 816      Im4 ~~     Im19   0.080 -0.005  -0.005   -0.026   -0.026
## 817      SAT =~      Im3   0.080  0.010   0.008    0.006    0.006
## 818      Im5 ~~     Im18   0.079  0.009   0.009    0.014    0.014
## 819     Im18 ~~    C_CR4   0.079 -0.013  -0.013   -0.016   -0.016
## 820     Im12 ~~     Im18   0.077 -0.007  -0.007   -0.017   -0.017
## 821     Im20 ~~    C_CR3   0.076 -0.016  -0.016   -0.017   -0.017
## 822       RI =~     Im17   0.075  0.019   0.011    0.009    0.009
## 823     Im18 ~~    SAT_2   0.074  0.007   0.007    0.016    0.016
## 824      Im8  ~    BRAND   0.071 -0.009  -0.011   -0.011   -0.011
## 825    SAT_1 ~~   C_REP3   0.070  0.003   0.003    0.016    0.016
## 826    SAT_3 ~~   C_REP1   0.070 -0.005  -0.005   -0.014   -0.014
## 827      Im4 ~~    SAT_3   0.068  0.006   0.006    0.019    0.019
## 828     FOOD =~     Im17   0.066  0.013   0.011    0.009    0.009
## 829   FRENCH =~   C_REP3   0.066 -0.005  -0.005   -0.009   -0.009
## 830     FOOD =~     Im18   0.066 -0.013  -0.011   -0.008   -0.008
## 831     Im19 ~~    C_CR4   0.066  0.012   0.012    0.017    0.017
## 832   CHOICE  ~      Im9   0.064 -0.008  -0.007   -0.009   -0.007
## 833      COI =~     Im20   0.061  0.007   0.012    0.008    0.008
## 834     Im20 ~~     Im12   0.060  0.007   0.007    0.016    0.016
## 835      Im4 ~~     Im21   0.060  0.005   0.005    0.018    0.018
## 836     Im21 ~~     Im13   0.058 -0.008  -0.008   -0.014   -0.014
## 837     Im13 ~~    SAT_1   0.057 -0.005  -0.005   -0.017   -0.017
## 838       RI =~    C_CR3   0.057  0.027   0.016    0.008    0.008
## 839      Im4 ~~     Im20   0.056 -0.005  -0.005   -0.019   -0.019
## 840     Im20 ~~     Im16   0.056  0.009   0.009    0.014    0.014
## 841    SAT_2 ~~   C_REP2   0.055  0.003   0.003    0.020    0.020
## 842     Im11 ~~    SAT_3   0.053 -0.009  -0.009   -0.012   -0.012
## 843     Im16 ~~   COM_A2   0.053 -0.009  -0.009   -0.013   -0.013
## 844    SAT_1 ~~    SAT_2   0.053  0.013   0.013    0.042    0.042
## 845     Im14 ~~     Im19   0.052  0.003   0.003    0.021    0.021
## 846      Im2 ~~    C_CR3   0.052  0.009   0.009    0.013    0.013
## 847      Im1 ~~     Im19   0.052 -0.005  -0.005   -0.030   -0.030
## 848      Im6 ~~   C_REP1   0.048 -0.003  -0.003   -0.011   -0.011
## 849    BRAND =~    C_CR3   0.048 -0.012  -0.014   -0.007   -0.007
## 850     Im10 ~~   C_REP2   0.047 -0.001  -0.001   -0.019   -0.019
## 851     FOOD =~      Im3   0.045 -0.007  -0.006   -0.005   -0.005
## 852      Im1 ~~   C_REP1   0.045 -0.003  -0.003   -0.022   -0.022
## 853     Im21 ~~   COM_A3   0.044 -0.009  -0.009   -0.011   -0.011
## 854   C_REP1 ~~    C_CR1   0.043 -0.006  -0.006   -0.012   -0.012
## 855      Im3 ~~     Im13   0.042  0.004   0.004    0.014    0.014
## 856     Im18 ~~   COM_A4   0.041 -0.008  -0.008   -0.011   -0.011
## 857     DECO  ~       RI   0.041  0.124   0.058    0.058    0.058
## 858   COM_A2 ~~   C_REP1   0.040  0.004   0.004    0.011    0.011
## 859     Im11 ~~     Im19   0.039 -0.006  -0.006   -0.012   -0.012
## 860     FOOD =~    C_CR3   0.039 -0.016  -0.013   -0.006   -0.006
## 861    C_CR1 ~~    C_CR4   0.038 -0.047  -0.047   -0.038   -0.038
## 862      Im1 ~~    C_CR4   0.037 -0.007  -0.007   -0.021   -0.021
## 863   CHOICE =~    SAT_3   0.037  0.007   0.009    0.009    0.009
## 864 PRODQUAL =~     Im21   0.036  0.014   0.010    0.007    0.007
## 865     Im11 ~~    C_CR3   0.034  0.011   0.011    0.010    0.010
## 866     Im20 ~~    C_CR4   0.033 -0.010  -0.010   -0.011   -0.011
## 867    AFCOM =~      Im3   0.033 -0.004  -0.005   -0.004   -0.004
## 868     Im12 ~~     Im19   0.033 -0.004  -0.004   -0.014   -0.014
## 869     DECO =~     Im16   0.032 -0.011  -0.014   -0.011   -0.011
## 870     DECO =~     Im19   0.032  0.011   0.014    0.012    0.012
## 871      Im3 ~~     Im16   0.031 -0.004  -0.004   -0.011   -0.011
## 872      COI =~     Im17   0.030 -0.004  -0.007   -0.005   -0.005
## 873      Im3 ~~     Im21   0.030 -0.004  -0.004   -0.010   -0.010
## 874      COI =~      Im6   0.030 -0.004  -0.006   -0.005   -0.005
## 875     Im18 ~~   COM_A3   0.029  0.006   0.006    0.009    0.009
## 876     Im19 ~~      Im6   0.029 -0.004  -0.004   -0.010   -0.010
## 877      Im5 ~~     Im10   0.029 -0.003  -0.003   -0.010   -0.010
## 878     Im13 ~~    C_CR4   0.028  0.008   0.008    0.011    0.011
## 879     Im13 ~~    C_CR1   0.027 -0.007  -0.007   -0.011   -0.011
## 880    ATMOS  ~       RI   0.026  0.113   0.053    0.053    0.053
## 881 PRODQUAL  ~      Im8   0.026  0.004   0.006    0.006    0.006
## 882      Im2 ~~    SAT_3   0.026 -0.004  -0.004   -0.009   -0.009
## 883     Im16 ~~   C_REP2   0.025  0.002   0.002    0.013    0.013
## 884      COI =~     Im14   0.024 -0.002  -0.003   -0.004   -0.004
## 885    C_CR3 ~~    C_CR4   0.023 -0.037  -0.037   -0.027   -0.027
## 886      COI =~   COM_A2   0.023  0.005   0.008    0.005    0.005
## 887      Im3 ~~   C_REP1   0.022  0.002   0.002    0.009    0.009
## 888      Im5 ~~   C_REP3   0.022  0.002   0.002    0.007    0.007
## 889      Im6 ~~   COM_A4   0.021 -0.005  -0.005   -0.008   -0.008
## 890      Im3 ~~     Im14   0.020 -0.001  -0.001   -0.012   -0.012
## 891      Im3 ~~     Im10   0.018  0.001   0.001    0.009    0.009
## 892   C_REP1 ~~    C_CR4   0.017 -0.004  -0.004   -0.007   -0.007
## 893      Im5 ~~    C_CR1   0.017  0.007   0.007    0.008    0.008
## 894      COI =~     Im10   0.017  0.002   0.003    0.003    0.003
## 895      Im3 ~~      Im6   0.017  0.002   0.002    0.008    0.008
## 896     Im10 ~~      Im1   0.017 -0.001  -0.001   -0.015   -0.015
## 897     DECO =~     Im14   0.015  0.002   0.003    0.004    0.004
## 898     DECO =~     Im10   0.015 -0.002  -0.003   -0.003   -0.003
## 899     DECO =~   COM_A4   0.013  0.005   0.006    0.004    0.004
## 900     Im22 ~~    C_CR4   0.013  0.006   0.006    0.008    0.008
## 901      Im4 ~~   C_REP1   0.013 -0.001  -0.001   -0.009   -0.009
## 902      SAT =~     Im19   0.013  0.009   0.007    0.007    0.007
## 903    AFCOM =~     Im13   0.012  0.004   0.004    0.004    0.004
## 904     Im21 ~~     Im19   0.011  0.003   0.003    0.007    0.007
## 905   COM_A3 ~~    C_CR4   0.011  0.007   0.007    0.006    0.006
## 906   FRENCH =~     Im10   0.010 -0.004  -0.004   -0.004   -0.004
## 907   FRENCH =~     Im14   0.010  0.004   0.004    0.005    0.005
## 908     Im10 ~~   C_REP1   0.009  0.001   0.001    0.006    0.006
## 909      COI =~      Im7   0.009  0.002   0.004    0.003    0.003
## 910     PROF =~     Im10   0.009  0.003   0.003    0.003    0.003
## 911     PROF =~     Im14   0.009 -0.003  -0.003   -0.003   -0.003
## 912    BRAND =~   COM_A1   0.009 -0.004  -0.004   -0.003   -0.003
## 913 PRODQUAL =~    SAT_3   0.007  0.006   0.004    0.004    0.004
## 914     Im21 ~~    SAT_1   0.007 -0.002  -0.002   -0.005   -0.005
## 915      Im7 ~~    C_CR3   0.006 -0.004  -0.004   -0.009   -0.009
## 916      SAT =~     Im16   0.006 -0.006  -0.005   -0.004   -0.004
## 917 PRODQUAL =~    C_CR3   0.006 -0.007  -0.005   -0.002   -0.002
## 918     Im19 ~~    C_CR1   0.006 -0.003  -0.003   -0.005   -0.005
## 919      Im4 ~~     Im10   0.005 -0.001  -0.001   -0.006   -0.006
## 920       RI =~      Im3   0.005  0.003   0.002    0.001    0.001
## 921     Im16 ~~      Im6   0.005 -0.002  -0.002   -0.004   -0.004
## 922   COM_A4 ~~    C_CR1   0.004  0.004   0.004    0.004    0.004
## 923     FOOD =~     Im12   0.004 -0.003  -0.003   -0.002   -0.002
## 924   FRENCH =~     Im12   0.003 -0.002  -0.002   -0.002   -0.002
## 925 PRODQUAL =~   C_REP1   0.003  0.002   0.001    0.002    0.002
## 926      COI =~     Im18   0.003  0.001   0.002    0.002    0.002
## 927     DECO =~     Im21   0.003 -0.002  -0.003   -0.002   -0.002
## 928     Im21 ~~      Im6   0.002 -0.002  -0.002   -0.003   -0.003
## 929      Im4 ~~     Im13   0.002 -0.001  -0.001   -0.004   -0.004
## 930   FRENCH =~      Im4   0.002  0.001   0.001    0.001    0.001
## 931     Im13 ~~   C_REP3   0.002  0.001   0.001    0.003    0.003
## 932    BRAND =~     Im21   0.002 -0.002  -0.002   -0.002   -0.002
## 933    ATMOS =~      Im6   0.001  0.001   0.002    0.001    0.001
## 934    ATMOS =~      Im7   0.001 -0.002  -0.002   -0.002   -0.002
## 935     Im18 ~~    SAT_3   0.001  0.001   0.001    0.002    0.002
## 936      Im6 ~~    C_CR3   0.001 -0.002  -0.002   -0.002   -0.002
## 937     Im11 ~~   C_REP3   0.001 -0.001  -0.001   -0.002   -0.002
## 938      Im5 ~~     Im13   0.001 -0.001  -0.001   -0.002   -0.002
## 939     Im14 ~~   COM_A4   0.001  0.001   0.001    0.002    0.002
## 940     Im12 ~~      Im1   0.001  0.001   0.001    0.003    0.003
## 941     Im16 ~~     Im17   0.000  0.001   0.001    0.002    0.002
## 942      Im1 ~~      Im7   0.000  0.000   0.000    0.004    0.004
## 943      Im5 ~~   COM_A3   0.000  0.001   0.001    0.001    0.001
## 944      Im5 ~~     Im20   0.000  0.000   0.000   -0.001   -0.001
## 945     Im21 ~~   C_REP2   0.000  0.000   0.000    0.000    0.000
## 946      Im9  ~     Im15   0.000  0.000   0.000    0.000    0.000
## 947      Im8 ~~      Im8   0.000  0.000   0.000    0.000    0.000
## 948      Im8 ~~     Im15   0.000  0.000   0.000       NA    0.000
## 949      Im8  ~     Im15   0.000  0.000   0.000    0.000    0.000
## 950     Im15  ~      Im8   0.000  0.000   0.000    0.000    0.000
## 951      Im8  ~      Im9   0.000  0.000   0.000    0.000    0.000
## 952     Im15  ~      Im9   0.000  0.000   0.000    0.000    0.000

2.5 Path analysis

parameterestimates(SEM_fit, boot.ci.type = "bca.simple", standardized = TRUE) |>
  arrange(-std.all,pvalue) |> filter(label!="") |>
  stable()

lhs	op	rhs	label	est	se	z	pvalue	ci.lower	ci.upper	std.lv	std.all	std.nox
SAT	~	PROF	s6	0.40	0.09	4.45	0.00	0.23	0.58	0.44	0.44	0.44
AFCOM	~	ATMOS	a3	0.37	0.05	6.93	0.00	0.27	0.48	0.42	0.42	0.42
COI	~	AFCOM	ca	0.54	0.09	5.81	0.00	0.36	0.72	0.36	0.36	0.36
RI	~	AFCOM	ra	0.19	0.03	6.16	0.00	0.13	0.24	0.35	0.35	0.35
RI	~	SAT	rs	0.19	0.04	4.32	0.00	0.10	0.28	0.28	0.28	0.28
ATMOStoCOI	:=	c03+css3+caa3	ATMOStoCOI	0.34	0.09	3.80	0.00	0.16	0.51	0.25	0.25	0.25
ATMOStoRI	:=	r03+rss3+raa3	ATMOStoRI	0.11	0.03	3.97	0.00	0.06	0.17	0.25	0.25	0.25
SAT	~	CHOICE	s5	0.12	0.04	2.78	0.01	0.03	0.20	0.18	0.18	0.18
caa3	:=	ca*a3	caa3	0.20	0.04	4.57	0.00	0.11	0.29	0.15	0.15	0.15
raa3	:=	ra*a3	raa3	0.07	0.01	4.72	0.00	0.04	0.10	0.15	0.15	0.15
AFCOM	~	FRENCH	a8	0.16	0.08	2.10	0.04	0.01	0.31	0.14	0.14	0.14
RI	~	PRODQUAL	r04	0.12	0.05	2.20	0.03	0.01	0.22	0.14	0.14	0.14
PROFtoRI	:=	r06+rss6+raa6	PROFtoRI	0.08	0.06	1.34	0.18	-0.04	0.20	0.13	0.13	0.13
rss6	:=	rs*s6	rss6	0.08	0.03	3.07	0.00	0.03	0.13	0.12	0.12	0.12
COI	~	PRODQUAL	c04	0.26	0.17	1.55	0.12	-0.07	0.59	0.11	0.11	0.11
COI	~	ATMOS	c03	0.15	0.09	1.59	0.11	-0.03	0.33	0.11	0.11	0.11
AFCOM	~	PROF	a6	0.13	0.11	1.14	0.25	-0.09	0.35	0.11	0.11	0.11
AFCOM	~	CHOICE	a5	0.09	0.06	1.55	0.12	-0.02	0.19	0.10	0.10	0.10
SAT	~	FRENCH	s8	0.08	0.06	1.30	0.19	-0.04	0.19	0.09	0.09	0.09
PQUALtoRI	:=	r04+rss4+raa4	PQUALtoRI	0.07	0.06	1.28	0.20	-0.04	0.18	0.09	0.09	0.09
RI	~	Im8	r0i8	0.05	0.04	1.28	0.20	-0.03	0.12	0.08	0.08	0.08
RI	~	ATMOS	r03	0.04	0.03	1.34	0.18	-0.02	0.10	0.08	0.08	0.08
SAT	~	Im15	si15	0.06	0.05	1.25	0.21	-0.03	0.15	0.07	0.08	0.07
SAT	~	FOOD	s2	0.08	0.07	1.05	0.29	-0.07	0.22	0.07	0.07	0.07
PQUALtoCOI	:=	c04+css4+caa4	PQUALtoCOI	0.17	0.17	0.98	0.33	-0.17	0.51	0.07	0.07	0.07
AFCOM	~	Im8	ai8	0.07	0.07	0.93	0.35	-0.07	0.21	0.06	0.06	0.06
SAT	~	ATMOS	s3	0.03	0.04	0.88	0.38	-0.04	0.11	0.05	0.05	0.05
caa8	:=	ca*a8	caa8	0.09	0.04	1.97	0.05	0.00	0.17	0.05	0.05	0.05
raa8	:=	ra*a8	raa8	0.03	0.02	1.99	0.05	0.00	0.06	0.05	0.05	0.05
rss5	:=	rs*s5	rss5	0.02	0.01	2.37	0.02	0.00	0.04	0.05	0.05	0.05
SAT	~	Im8	si8	0.03	0.05	0.59	0.55	-0.07	0.14	0.04	0.04	0.04
CHOICEtoRI	:=	r05+rss5+raa5	CHOICEtoRI	0.02	0.03	0.61	0.54	-0.04	0.08	0.04	0.04	0.04
caa6	:=	ca*a6	caa6	0.07	0.06	1.11	0.27	-0.05	0.19	0.04	0.04	0.04
raa6	:=	ra*a6	raa6	0.02	0.02	1.12	0.26	-0.02	0.07	0.04	0.04	0.04
caa5	:=	ca*a5	caa5	0.05	0.03	1.51	0.13	-0.01	0.11	0.04	0.04	0.04
raa5	:=	ra*a5	raa5	0.02	0.01	1.51	0.13	0.00	0.04	0.04	0.04	0.04
FOODtoRI	:=	r02+rss2+raa2	FOODtoRI	0.03	0.05	0.48	0.63	-0.08	0.13	0.04	0.04	0.04
DECOtoCOI	:=	c01+css1+caa1	DECOtoCOI	0.04	0.10	0.41	0.68	-0.15	0.23	0.03	0.03	0.03
SAT	~	BRAND	s7	0.02	0.05	0.42	0.67	-0.07	0.11	0.03	0.03	0.03
AFCOM	~	Im9	ai9	0.02	0.04	0.51	0.61	-0.06	0.11	0.02	0.03	0.02
css1	:=	cs*s1	css1	0.04	0.02	1.74	0.08	0.00	0.08	0.03	0.03	0.03
COI	~	BRAND	c07	0.04	0.10	0.38	0.71	-0.15	0.23	0.03	0.03	0.03
AFCOM	~	Im15	ai15	0.02	0.06	0.40	0.69	-0.09	0.14	0.02	0.03	0.02
rss8	:=	rs*s8	rss8	0.01	0.01	1.25	0.21	-0.01	0.04	0.02	0.02	0.02
rss2	:=	rs*s2	rss2	0.01	0.01	1.02	0.31	-0.01	0.04	0.02	0.02	0.02
BRANDtoRI	:=	r07+rss7+raa7	BRANDtoRI	0.01	0.03	0.25	0.80	-0.06	0.07	0.02	0.02	0.02
RI	~	BRAND	r07	0.01	0.03	0.24	0.81	-0.05	0.07	0.02	0.02	0.02
BRANDtoCOI	:=	c07+css7+caa7	BRANDtoCOI	0.02	0.10	0.20	0.84	-0.18	0.22	0.01	0.01	0.01
rss3	:=	rs*s3	rss3	0.01	0.01	0.87	0.39	-0.01	0.02	0.01	0.01	0.01
RI	~	DECO	r01	0.01	0.03	0.23	0.82	-0.05	0.06	0.01	0.01	0.01
FRENCHtoRI	:=	r08+rss8+raa8	FRENCHtoRI	0.01	0.04	0.19	0.85	-0.07	0.09	0.01	0.01	0.01
RI	~	FOOD	r02	0.01	0.05	0.18	0.86	-0.09	0.10	0.01	0.01	0.01
COI	~	DECO	c01	0.01	0.09	0.16	0.88	-0.17	0.20	0.01	0.01	0.01
rss7	:=	rs*s7	rss7	0.00	0.01	0.42	0.68	-0.01	0.02	0.01	0.01	0.01
css4	:=	cs*s4	css4	0.02	0.03	0.55	0.58	-0.04	0.07	0.01	0.01	0.01
AFCOM	~	FOOD	a2	0.01	0.10	0.09	0.93	-0.18	0.20	0.01	0.01	0.01
SAT	~	Im9	si9	0.00	0.03	0.07	0.94	-0.06	0.07	0.00	0.00	0.00
caa2	:=	ca*a2	caa2	0.00	0.05	0.09	0.93	-0.10	0.11	0.00	0.00	0.00
raa2	:=	ra*a2	raa2	0.00	0.02	0.09	0.93	-0.03	0.04	0.00	0.00	0.00
CHOICEtoCOI	:=	c05+css5+caa5	CHOICEtoCOI	0.00	0.09	-0.01	0.99	-0.18	0.18	0.00	0.00	0.00
COI	~	CHOICE	c05	0.00	0.09	-0.05	0.96	-0.18	0.17	0.00	0.00	0.00
css7	:=	cs*s7	css7	-0.01	0.02	-0.42	0.68	-0.04	0.03	-0.01	-0.01	-0.01
raa7	:=	ra*a7	raa7	0.00	0.01	-0.27	0.79	-0.02	0.02	-0.01	-0.01	-0.01
caa7	:=	ca*a7	caa7	-0.01	0.03	-0.27	0.79	-0.07	0.05	-0.01	-0.01	-0.01
raa1	:=	ra*a1	raa1	0.00	0.01	-0.36	0.72	-0.02	0.02	-0.01	-0.01	-0.01
caa1	:=	ca*a1	caa1	-0.01	0.03	-0.36	0.72	-0.07	0.05	-0.01	-0.01	-0.01
css3	:=	cs*s3	css3	-0.01	0.02	-0.83	0.40	-0.04	0.02	-0.01	-0.01	-0.01
RI	~	Im15	r0i15	0.00	0.03	-0.15	0.88	-0.06	0.06	-0.01	-0.01	-0.01
COI	~	Im8	c0i8	-0.02	0.12	-0.14	0.89	-0.24	0.21	-0.01	-0.01	-0.01
rss4	:=	rs*s4	rss4	-0.01	0.02	-0.55	0.58	-0.04	0.02	-0.01	-0.01	-0.01
COI	~	Im9	c0i9	-0.02	0.07	-0.22	0.82	-0.16	0.12	-0.01	-0.01	-0.01
css2	:=	cs*s2	css2	-0.03	0.03	-0.98	0.33	-0.08	0.03	-0.01	-0.01	-0.01
css8	:=	cs*s8	css8	-0.03	0.02	-1.18	0.24	-0.07	0.02	-0.02	-0.02	-0.02
AFCOM	~	BRAND	a7	-0.02	0.06	-0.27	0.79	-0.13	0.10	-0.02	-0.02	-0.02
AFCOM	~	DECO	a1	-0.02	0.06	-0.36	0.72	-0.13	0.09	-0.02	-0.02	-0.02
FREMCHtoCOI	:=	c08+css8+caa8	FREMCHtoCOI	-0.05	0.13	-0.37	0.71	-0.30	0.21	-0.03	-0.03	-0.03
COI	~	FOOD	c02	-0.06	0.15	-0.38	0.71	-0.36	0.24	-0.03	-0.03	-0.03
RI	~	PROF	r06	-0.02	0.06	-0.31	0.76	-0.14	0.10	-0.03	-0.03	-0.03
css5	:=	cs*s5	css5	-0.04	0.02	-1.93	0.05	-0.09	0.00	-0.03	-0.03	-0.03
DECOtoRI	:=	r01+rss1+raa1	DECOtoRI	-0.02	0.03	-0.52	0.60	-0.08	0.04	-0.03	-0.03	-0.03
SAT	~	PRODQUAL	s4	-0.04	0.08	-0.56	0.58	-0.20	0.11	-0.04	-0.04	-0.04
FOODtoCOI	:=	c02+css2+caa2	FOODtoCOI	-0.08	0.16	-0.50	0.61	-0.40	0.23	-0.04	-0.04	-0.04
rss1	:=	rs*s1	rss1	-0.02	0.01	-1.98	0.05	-0.04	0.00	-0.04	-0.04	-0.04
COI	~	Im15	c0i15	-0.06	0.10	-0.58	0.56	-0.25	0.14	-0.03	-0.04	-0.03
raa4	:=	ra*a4	raa4	-0.04	0.02	-1.79	0.07	-0.08	0.00	-0.04	-0.04	-0.04
caa4	:=	ca*a4	caa4	-0.10	0.06	-1.78	0.08	-0.22	0.01	-0.04	-0.04	-0.04
RI	~	CHOICE	r05	-0.02	0.03	-0.74	0.46	-0.07	0.03	-0.04	-0.04	-0.04
RI	~	FRENCH	r08	-0.04	0.04	-0.94	0.35	-0.11	0.04	-0.06	-0.06	-0.06
COI	~	FRENCH	c08	-0.11	0.12	-0.86	0.39	-0.35	0.14	-0.06	-0.06	-0.06
css6	:=	cs*s6	css6	-0.15	0.06	-2.35	0.02	-0.27	-0.02	-0.08	-0.08	-0.08
RI	~	Im9	r0i9	-0.05	0.02	-2.11	0.03	-0.09	0.00	-0.08	-0.11	-0.08
COI	~	PROF	c06	-0.20	0.19	-1.03	0.30	-0.58	0.18	-0.11	-0.11	-0.11
AFCOM	~	PRODQUAL	a4	-0.19	0.10	-1.88	0.06	-0.40	0.01	-0.12	-0.12	-0.12
SAT	~	DECO	s1	-0.10	0.04	-2.24	0.02	-0.18	-0.01	-0.14	-0.14	-0.14
PROFtoCOI	:=	c06+css6+caa6	PROFtoCOI	-0.28	0.19	-1.49	0.14	-0.64	0.09	-0.15	-0.15	-0.15
COI	~	SAT	cs	-0.36	0.13	-2.71	0.01	-0.62	-0.10	-0.18	-0.18	-0.18

Case Study 3: Galeries Lafayette

UNIGE - GSEM - Advanced Data-Driven Decision Making

2023-05-01

1 Setup

1.1 libraries

1.2 Load data

1.3 labels

1.4 Clean and handle missing data

1.5 Explore Data

2 Dimensions by which Galeries Lafayette is perceived

2.1 ROUND 1: Exploratory factor analysis

2.1.1 Variable selection for EFA

2.1.2 handle missing data

2.1.3 Check adequacy of correlation Matrix

2.1.3.1 correlation matrix

2.1.3.2 Bartlett’s Test

2.1.3.3 KMO

2.1.3.4 Anti-image Correlation

2.1.4 Select method: PAF

2.1.4.1 Extract factors

2.1.4.1.1 Scree plot

2.1.4.1.2 Kaiser Criterion

2.1.4.1.3 Total Variance Explained

2.1.4.2 Determine number of factors to retain

2.1.4.3 PAF orthogonal Varimax with n factors

2.1.4.3.1 Communalities

Number of factors = 5

Number of factors = 6

Number of factors = 7

Number of factors = 8

2.1.4.3.2 Factor loadings

Number of factors = 5

Number of factors = 6

Number of factors = 7

Number of factors = 8

2.1.4.4 PAF oblique Promax with n factors

2.1.4.4.1 Communalities

Number of factors = 5

Number of factors = 6

Number of factors = 7

Number of factors = 8

2.1.4.4.2 Factor loadings

Number of factors = 5

Number of factors = 6

Number of factors = 7

Number of factors = 8

2.2 ROUND 2 : Exploratory factor analysis round 2

2.2.1 Variable selection for EFA

2.2.2 handle missing data

2.2.3 Check adequacy of correlation Matrix

2.2.3.1 correlation matrix

2.2.3.2 Bartlett’s Test

2.2.3.3 KMO

2.2.3.4 Anti-image Correlation

2.2.4 Select method: PAF

2.2.4.1 Extract factors

2.2.4.1.1 Scree plot

2.2.4.1.2 Kaiser Criterion

2.2.4.1.3 Total Variance Explained

2.2.4.2 Determine number of factors to retain

2.2.4.3 PAF orthogonal Varimax with n factors

2.2.4.3.1 Communalities

Number of factors = 5

Number of factors = 6

Number of factors = 7

Number of factors = 8

2.2.4.3.2 Factor loadings

Number of factors = 5

Number of factors = 6

Number of factors = 7

Number of factors = 8

2.2.4.4 PAF oblique Promax with n factors

2.2.4.4.1 Communalities

Number of factors = 5

Number of factors = 6

Number of factors = 7

Number of factors = 8

2.2.4.4.2 Factor loadings

Number of factors = 5

Number of factors = 6